- \n
- Probability Maintaining Mathematical Proficiency<\/a><\/li>\n
- Probability Monitoring Progress<\/a><\/li>\n<\/ul>\n
Lesson: 1 Sample Spaces and Probability<\/strong><\/p>\n
- \n
- 12.1 Sample Spaces and Probability<\/a><\/li>\n
- Lesson 12.1 Sample Spaces and Probability<\/a><\/li>\n
- Exercise 12.1 Sample Spaces and Probability<\/a><\/li>\n<\/ul>\n
Lesson: 2 Independent and Dependent Events<\/strong><\/p>\n
- \n
- 12.2 Independent and Dependent Events<\/a><\/li>\n
- Lesson 12.2 Independent and Dependent Events<\/a><\/li>\n
- Exercise 12.2 Independent and Dependent Events<\/a><\/li>\n<\/ul>\n
Lesson: 3 Two-Way Tables and Probability<\/strong><\/p>\n
- \n
- 12.3 Two-Way Tables and Probability<\/a><\/li>\n
- Lesson 12.3 Two-Way Tables and Probability<\/a><\/li>\n
- Exercise 12.3 Two-Way Tables and Probability<\/a><\/li>\n<\/ul>\n
Quiz<\/strong><\/p>\n
- \n
- 12.1 – 12.3 Quiz<\/a><\/li>\n<\/ul>\n
Lesson: 4 Probability of Disjoint and Overlapping Events<\/strong><\/p>\n
- \n
- 12.4 Probability of Disjoint and Overlapping Events<\/a><\/li>\n
- Lesson 12.4 Probability of Disjoint and Overlapping Events<\/a><\/li>\n
- Exercise 12.4 Probability of Disjoint and Overlapping Events<\/a><\/li>\n<\/ul>\n
Lesson: 5 Permutations and Combinations<\/strong><\/p>\n
- \n
- 12.5 Permutations and Combinations<\/a><\/li>\n
- Lesson 12.5 Permutations and Combinations<\/a><\/li>\n
- Exercise 12.5 Permutations and Combinations<\/a><\/li>\n<\/ul>\n
Lesson: 6 Binomial Distributions<\/strong><\/p>\n
- \n
- 12.6 Binomial Distributions<\/a><\/li>\n
- Lesson 12.6 Binomial Distributions<\/a><\/li>\n
- Exercise 12.6 Binomial Distributions<\/a><\/li>\n<\/ul>\n
Chapter: 12 –\u00a0Probability\u00a0<\/strong><\/p>\n
- \n
- Probability Review<\/a><\/li>\n
- Probability Test<\/a><\/li>\n
- Probability Cumulative Assessment<\/a><\/li>\n<\/ul>\n
<\/a>Probability Maintaining Mathematical Proficiency<\/h3>\n
Write and solve a proportion to answer the question.<\/p>\n
Question 1.
\nWhat percent of 30 is 6?
\nAnswer: 20<\/p>\nExplanation:
\n100% = 30
\nx% = 6
\n100% = 30(1)
\nx% = 6(2)
\n100%\/x% = 30\/6
\nTaking the inverse of both sides
\nx%\/100% = 6\/30
\nx = 20%
\nThus 6 is 20% of 30.<\/p>\nQuestion 2.
\nWhat number is 68% of 25?
\nAnswer: 17<\/p>\nExplanation:
\n68% \u00d7 25
\n(68 \u00f7 100) \u00d7 25
\n(68 \u00d7 25) \u00f7 100
\n1700 \u00f7 100 = 17<\/p>\nQuestion 3.
\n34.4 is what percent of 86?
\nAnswer: 40<\/p>\nExplanation:
\n100% = 86
\nx% = 34.4
\n100% = 86(1)
\nx% = 34.4(2)
\n100%\/x% = 86\/34.4
\nTaking the inverse of both sides
\nx%\/100% = 34.4\/86
\nx = 40%
\nTherefore, 34.4 is 40% of 86.<\/p>\nDisplay the data in a histogram.<\/p>\n
Question 4.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-1.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-img_1-300x242.png\")
<\/p>\nQuestion 5.
\nABSTRACT REASONING<\/strong>
\nYou want to purchase either a sofa or an arm chair at a furniture store. Each item has the same retail price. The sofa is 20% off. The arm chair is 10% off. and you have a coupon to get an additional 10% off the discounted price of the chair. Are the items equally priced after the discounts arc applied? Explain.
\nAnswer: Yes<\/p>\nExplanation:
\nYou want to purchase either a sofa or an armchair at a furniture store.
\nEach item has the same retail price. The sofa is 20% off. The armchair is 10% off. and you have a coupon to get an additional 10% off the discounted price of the chair.
\nThe price of armchair and sofa are the same.
\nIf you add 10% to chair the discount for the chair and sofa will be the same.
\n10% + 10% = 20%<\/p>\n<\/a>Probability Monitoring Progress<\/h3>\n
In Exercises 1 and 2, describe the event as unlikely, equally likely to happen or not happen, or likely. Explain your reasoning.<\/p>\n
Question 1.
\nThe oldest child in a family is a girl.
\nAnswer:<\/p>\nQuestion 2.
\nThe two oldest children in a family with three children are girls.
\nAnswer:<\/p>\nQuestion 3.
\nGive an example of an event that is certain to occur.
\nAnswer:
\nIf A and B are independent event
\nP(A) = 1\/2
\nP(B) = 1\/5
\nP(A and B) = P(A) \u00d7 P(B)
\n= 1\/2 \u00d7 1\/5
\n= 1\/10<\/p>\n<\/a>12.1 Sample Spaces and Probability<\/h3>\n
Exploration 1<\/strong><\/p>\n
Finding the Sample Space of an Experiment<\/p>\n
Work with a partner: In an experiment, three coins are flipped. List the possible outcomes in the sample space of the experiment.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-2.png\")
\nAnswer:
\nThe number of different outcomes when three coins are tossed is 2 \u00d7 2 \u00d7 2 = 8.
\nAll 8 possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH and TTT.<\/p>\nExploration 2<\/strong><\/p>\n
Finding the Sample Space of an Experiment<\/p>\n
Work with a partner: List the possible outcomes in the sample space of the experiment.<\/p>\n
a. One six-sided die is rolled.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-3.png\")
\nAnswer: 6 possible outcomes<\/p>\nb. Two six-sided die is rolled.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-4.png\")
\nAnswer:
\nRolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 . 6 or 36 equally likely outcomes.<\/p>\nExploration 3<\/h3>\n
Finding the Sample Space of an Experiment<\/p>\n
Work with a partner: In an experiment, a spinner is spun.<\/p>\n
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-5.png\")
<\/p>\na. How many ways can you spin a 1? 2? 3? 4? 5?
\nAnswer: 1, 2, 3, 2, 4<\/p>\nb. List the sample space.
\nAnswer: 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5<\/p>\nc. What is the total number of outcomes?
\nAnswer: 12<\/p>\nExploration 4<\/p>\n
Finding the Sample Space of an Experiment<\/p>\n
Work with a partner: In an experiment, a bag contains 2 blue marbles and 5 red marbles. Two marbles arc drawn from the bag.<\/p>\n
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-6.png\")
<\/p>\na. How many ways can you choose two blue? a red then blue? a blue then red? two red?
\nAnswer: BB – 2, RB – 10, BR – 10, RR – 20<\/p>\nb. List the sample space.
\nAnswer:<\/p>\nc. What is the total number of outcomes?
\nAnswer: 42<\/p>\nCommunicate Your Answer<\/p>\n
Question 5.
\nHow can you list the possible outcomes in the sample space of an experiment?
\nAnswer:
\nThere are four possible outcomes for each spin: red, blue, yellow, green. Then, multiply the number of outcomes by the number of spins. June flipped the coin three times. The answer is there are 12 outcomes in the sample space.<\/p>\nQuestion 6.
\nFor Exploration 3, find the ratio of the number of each possible outcome to the total number of outcomes. Then find the sum of these ratios. Repeat for Exploration 4. What do you observe?
\nLOOKING FOR A PATTERN<\/strong>
\nTo be proficient in math, you need to look closely to discern a pattern or structure.
\nAnswer:<\/p>\n<\/a>Lesson 12.1 Sample Spaces and Probability<\/h3>\n
Monitoring Progress<\/strong><\/p>\n
Find the number of possible outcomes in the sample space. Then list the possible outcomes.<\/p>\n
Question 1.
\nYou flip two coins.
\nAnswer: 4<\/p>\nExplanation:
\nWhen we flip two coins simultaneoulsy then the possible outcomes will be (H, H), (T, T), (T, H), (H, T)
\nwhere H represents heads
\nT represents tails.
\nThus the possible outcomes are 2\u00b2 = 4<\/p>\nQuestion 2.
\nYou flip two Coins and roll a six-sided die.
\nAnswer: 6 \u00d7 2\u00b2 = 24<\/p>\nExplanation:
\nWe roll a die and flip two coins. We have to find the number of possible outcomes in this space. Also we have to list the possible outcomes.
\n1 = {When rolling the dice, the number 1 fell};
\n2 = {When rolling the dice, the number 2 fell};
\n3 = {When rolling the dice, the number 3 fell};
\n4 = {When rolling the dice, the number 4 fell};
\n5 = {When rolling the dice, the number 5 fell};
\n6 = {When rolling the dice, the number 6 fell};
\nOn the other hand, using H for Heads and T for Tails we can list the outcomes.
\n(1, H, H), (2, H, H), (3, H, H), (4, H, H), (5, H, H), (6, H, H)
\n(1, T, H), (2, T, H), (3, T, H), (4, T, H), (5, T, H), (6, T, H)
\n(1, H, T), (2, H, T), (3, H, T), (4, H, T), (5, H, T), (6, H, T)
\n(1, T, T), (2, T, T), (3, T, T), (4, T, T), (5, T, T), (6, T, T)
\nTherefore, we can conclude that the number of all possible outcomes is
\n6 \u00d7 2\u00b2 = 24<\/p>\nQuestion 3.
\nYou flip a coin and roll a six-sided die. What is the probability that the coin shows tails and the die shows 4?
\nAnswer:
\nThe sample space has 12 possible outcomes.
\nHeads, 1
\nHeads, 2
\nHeads, 3
\nHeads, 4
\nHeads, 5
\nHeads, 6
\nTails, 1
\nTails, 2
\nTails, 3
\nTails, 4
\nTails, 5
\nTails, 6
\nProbability that the coin shows tails and the die shows 4 is 4\/12 = 1\/3<\/p>\nFind P(\\(\\bar{A}\\)).<\/p>\n
Question 4.
\nP(A) = 0.45
\nAnswer:
\nP(\\(\\bar{A}\\)) = 1 – P(A)
\nP(A) = 0.45
\nP(\\(\\bar{A}\\)) = 1 – 0.45
\nP(\\(\\bar{A}\\)) = 0.55<\/p>\nQuestion 5.
\nP(A) = \\(\\frac{1}{4}\\)
\nAnswer:
\nP(\\(\\bar{A}\\)) = 1 – P(A)
\nP(A) = \\(\\frac{1}{4}\\)
\nP(\\(\\bar{A}\\)) = 1 – \\(\\frac{1}{4}\\)
\nP(\\(\\bar{A}\\)) = \\(\\frac{3}{4}\\)<\/p>\nQuestion 6.
\nP(A) = 1
\nAnswer:
\nP(\\(\\bar{A}\\)) = 1 – P(A)
\nP(A) = 1
\nP(\\(\\bar{A}\\)) = 1 – 1
\nP(\\(\\bar{A}\\)) = 0<\/p>\nQuestion 7.
\nP(A) = 0.03
\nAnswer:
\nP(\\(\\bar{A}\\)) = 1 – P(A)
\nP(A) = 0.03
\nP(\\(\\bar{A}\\)) = 1 – 0.03
\nP(\\(\\bar{A}\\)) = 0.97<\/p>\nQuestion 8.
\nIn Example 4, are you more likely to get 10 points or 5 points?
\nAnswer:
\n10: 0.09
\n5: (5 – 10)\/324
\n= (36\u03c0 – 9\u03c0)\/324
\n= 27\u03c0\/324
\n= 0.26<\/p>\nQuestion 9.
\nIn Example 4, are you more likely to score points (10, 5, or 2) or get 0 points?
\nAnswer:
\n2: (2 – 5)\/324
\n= (81\u03c0 – 36\u03c0)\/324
\n= 45\u03c0\/324
\n= 0.43
\n0.09 + 0.26 + 0.43 = 0.78
\nMore likely to get 2 points.<\/p>\nQuestion 10.
\nIn Example 5, for which color is the experimental probability of stopping on the color greater than the theoretical probability?
\nAnswer:
\n9\/20 = 0.45<\/p>\nQuestion 11.
\nIn Example 6, what is the probability that a pet-owning adult chosen at random owns a fish?
\nAnswer:
\n146\/1328 = 73\/664 = 0.11<\/p>\n<\/a>Exercise 12.1 Sample Spaces and Probability<\/h3>\n
Vocabulary and Core Concept Check<\/p>\n
Question 1.
\nCOMPLETE THE SENTENCE<\/strong>
\nA number that describes the likelihood of an event is the ___________ of the event.
\nAnswer:
\nA number that describes the likelihood of an event is the Probability of the event.<\/p>\nQuestion 2.
\nWRITING<\/strong>
\nDescribe the difference between theoretical probability and experimental probability.
\nAnswer: Experimental probability is the result of an experiment. Theoretical probability is what is expected to happen.<\/p>\nMonitoring Progress and Modeling with Mathematics<\/p>\n
In Exercises 3 – 6. find the number of possible outcomes in the sample space. Then list the possible outcomes.<\/p>\n
Question 3.
\nYou roll a die and flip three coins.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-3.1.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-3.2.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-3.3.png\")
<\/p>\nQuestion 4.
\nYou flip a coin and draw a marble at random from a hag containing two purple marbles and one while marble.
\nAnswer:
\nGiven data,
\nYou flip a coin and draw a marble at random from a hag containing two purple marbles and one while marble.
\nthe probability of getting a purple marble = 2\/3
\nthe probability of getting a white marble = 1\/3<\/p>\nQuestion 5.
\nA bag contains four red cards numbered 1 through 4, four white cards numbered 1 through 4, and four black cards numbered 1 through 4. You choose a card at random.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-5.png\")
<\/p>\nQuestion 6.
\nYou draw two marbles without replacement from a bag containing three green marbles and four black marbles.
\nAnswer:
\nIn all there are 7 marbles when you first grab a marble, after that you take one marble away then you have 6 marbles to choose.
\n7 \u00d7 6 = 42
\n42 possible outcomes: GG, GG, GB, GB, GB, GB, GG, GG, GB, GB, GB, GB, GG, GG, GB, GB, GB, GB, BG, BG, BG, BB, BB, BB, BG, BG, BG, BB, BB, BB, BG, BG, BG, BB, BB, BB, BG, BG, BG, BB, BB, BB, BB.<\/p>\nQuestion 7.
\nPROBLEM SOLVING<\/strong>
\nA game show airs on television five days per week. Each day, a prize is randomly placed behind one of two doors. The contestant wins the prize by selecting the correct door. What is the probability that exactly two of the five contestants win a prize during a week?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-7.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-7.1.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-7.2.png\")
<\/p>\nQuestion 8.
\nPROBLEM SOLVING<\/strong>
\nYour friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades?
\nAnswer:
\nYou have two decks of 52 cards and in a normal deck, there are 13 cards of each suit.
\nSo there are 13 spades in the deck.
\nTherefore the probability of you drawing a spade is 13 out of all the 52 cards or \\(\\frac{13}{52}\\), which can be reduced to \\(\\frac{1}{4}\\). You do this two times with different decks that are exactly the same so you multiply \\(\\frac{1}{4}\\) times \\(\\frac{1}{4}\\). 1 times 1 is 1 and 4 times 4 is 16, so it is \\(\\frac{1}{16}\\).
\nYou can turn this into a percentage by dividing 1 by 16 and moving the decimal place to places to the right.
\n6.25% is the probability that you will draw two spades.<\/p>\nQuestion 9.
\nPROBLEM SOLVING<\/strong>
\nWhen two six-sided dice are rolled, there are 36 possible outcomes. Find the probability that
\n(a) the sum is not 4 and
\n(b) the sum is greater than 5.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-9.1.png\")
<\/p>\nQuestion 10.
\nPROBLEM SOLVING<\/strong>
\nThe age distribution of a population is shown. Find the probability of each event.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-8.png\")
\na. A person chosen at random is at least 15 years old.
\nAnswer: 80%<\/p>\nb. A person chosen at random is from 25 to 44 years old.
\nAnswer: 13% + 13% = 26%<\/p>\nQuestion 11.
\nERROR ANALYSIS<\/strong>
\nA student randomly, guesses the answers to two true-false questions. Describe and correct the error in finding the probability of the student guessing both answers correctly.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-9.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-11.png\")
<\/p>\nQuestion 12.
\nERROR ANALYSIS<\/strong>
\nA student randomly draws a number between 1 and 30. Describe and correct the error in finding the probability that the number drawn is greater than 4.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-10.png\")
\nAnswer:
\nThe error is that the probability of the complement of the event is 4\/30, not 3\/30, because if you are looking for a sum greater than 4, than you subtract 1 by numbers less than or equal to 4 by the total amount of numbers, which is 30.
\nP(Sum is greater than 4)=1-P(Sum is less than or equal to 4)
\n1 – 2\/15
\n= 13\/15<\/p>\nQuestion 13.
\nMATHEMATICAL CONNECTIONS<\/strong>
\nYou throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. What is the probability your dart lands in the yellow region?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-11.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-13.png\")
<\/p>\nQuestion 14.
\nMATHEMATICAL CONNECTIONS<\/strong>
\nThe map shows the length (in miles) of shoreline along the Gulf of Mexico for each state that borders the body of water. What is the probability that a ship coming ashore at a random point in the Gulf of Mexico lands in the given state?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.png\")
\na. Texas
\nAnswer:
\nBy using the above map we can solve the problem
\nTotal length of the shoreline: 367 + 397 + 44 + 53 + 770 = 1631 miles
\nThe probability of the ship landing in Texas: 367\/1631 = 0.23<\/p>\nb. Alabama
\nAnswer:
\nThe probability of the ship landing in Alabama: 53\/1631 = 0.03<\/p>\nc. Florida
\nAnswer:
\nThe probability of the ship landing in Florida: 770\/1631 = 0.47<\/p>\nd. Louisiana
\nAnswer:
\nThe probability of the ship landing in Louisiana: 397\/1631 = 0.24<\/p>\nQuestion 15.
\nDRAWING CONCLUSIONS<\/strong>
\nYou roll a six-sided die 60 times. The table shows the results. For which number is the experimental probability of rolling the number the same as the theoretical probability?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-13.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-15.png\")
<\/p>\nQuestion 16.
\nDRAWING CONCLUSIONS<\/strong>
\nA bag contains 5 marbles that are each a different color. A marble is drawn, its color is recorded, and then the marble is placed back in the hag. This process is repeated until 30 marbles have been drawn. The table shows the results. For which marble is the experimental probability of drawing the marble the same as the theoretical probability?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-14.png\")
\nAnswer:
\nTotal number of marbles = 30
\n6\/30 = 1\/5
\nFor black marble the experimental probability of drawing the marble the same as the theoretical probability.<\/p>\nQuestion 17.
\nREASONING<\/strong>
\nRefer to the spinner shown. The spinner is divided into sections with the same area.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-15.png\")
\na. What is the theoretical probability that the spinner stops on a multiple of 3?
\nb. You spin the spinner 30 times. If stops on a multiple of 3 twenty times. What is the experimental probability of Stopping on a multiple of 3?
\nc. Explain why the probability you found in part (b) is different than the probability you found in part (a).
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-17.png\")
<\/p>\nQuestion 18.
\nOPEN-ENDED<\/strong>
\nDescribe a real-life event that has a probability of 0. Then describe a real-life event that has a probability of 1.
\nAnswer:
\nThe probability of rolling a 7 with a standard 6-sided die = 0
\nThe probability of rolling a natural number with a standard 6-sided die = 1<\/p>\nQuestion 19.
\nDRAWING CONCLUSIONS<\/strong>
\nA survey of 2237 adults ages 18 and over asked which Sport 15 their favorite. The results are shown in the figure. What is the probability that an adult chosen at random prefers auto racing?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-16.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-19.png\")
<\/p>\nQuestion 20.
\nDRAWING CONCLUSIONS<\/strong>
\nA survey of 2392 adults ages 18 and over asked what type of food they Would be most likely to choose at a restaurant. The results are shown in the figure. What is the probability that an adult chosen at random prefers Italian food?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-17.png\")
\nAnswer:
\nP(Italian) = 526\/1196
\n= 263\/1196
\nP(Italian) \u2248 22%<\/p>\nQuestion 21.
\nANALYZING RELATIONSHIPS<\/strong>
\nRefer to the board in Exercise 13. Order the likelihoods that the dart lands in the given region from least likely to most likely.
\nA. green
\nB. not blue
\nC. red
\nD. not yellow
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-21.1.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-21.2.png\")
<\/p>\nQuestion 22.
\nANALYZING RELATIONSHIPS<\/strong>
\nRefer to the chart below. Order the following events from least likely to most likely.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-18.png\")
\nA. It rains on Sunday.
\nAnswer:
\n80%
\n= 80\/20 = 4\/1
\nThe ratio is 4:1<\/p>\nB. It does not rain on Saturday.
\nAnswer:
\n100 – 30 = 70%
\n= 30\/70 = 3 : 7<\/p>\nC. It rains on Monday.
\nAnswer: 90%
\n= 90\/10 = 9\/1
\n= 9 : 1<\/p>\nD. It does not rain on Friday.
\nAnswer:
\n100 – 5 = 95%
\n= 5\/95 = 1\/19
\n= 1 : 19<\/p>\nQuestion 23.
\nUSING TOOLS<\/strong>
\nUse the figure in Example 3 to answer each question.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-19.png\")
\na. List the possible sums that result from rolling two six-sided dice.
\nb. Find the theoretical probability of rolling each sum.
\nc. The table below shows a simulation of rolling two six-sided dice three times. Use a random number generator to simulate rolling two six-sided dice 50 times. Compare the experimental probabilities of rolling each sum with the theoretical probabilities.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-23.1.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-23.2.png\")
<\/p>\nQuestion 24.
\nMAKING AN ARGUMENT<\/strong>
\nYou flip a coin three times. It lands on heads twice and on tails once. Your friend concludes that the theoretical probability of the coin landing heads up is P(heads up) = \\(\\frac{2}{3}\\). Is your friend correct? Explain your reasoning.
\nAnswer:
\nThe friend is incorrect because the probability of heads here is \\(\\frac{2}{3}\\), is the experimental probabiility of heads for this particular case, while its theoretical probability will always be \\(\\frac{1}{2}\\).<\/p>\nQuestion 25.
\nMATHEMATICAL CONNECTIONS<\/strong>
\nA sphere fits inside a cube so that it touches each side, as shown. What is the probability a point chosen at random inside the cube is also inside the sphere ?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-20.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-25.1.png\")
<\/p>\nQuestion 26.
\nHOW DO YOU SEE IT?<\/strong>
\nConsider the graph of f shown. What is the probability that the graph of y = f(x) + c intersects the x-axis when c is a randomly chosen integer from 1 to 6? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-21.png\")
\nAnswer:<\/p>\nQuestion 27.
\nDRAWING CONCLUSIONS<\/strong>
\nA manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Predict the number of computers with defects in a shipment of 15,000 computers. Explain your reasoning.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-27.png\")
<\/p>\nQuestion 28.
\nTHOUGHT PROVOKING<\/strong>
\nThe tree diagram shows a sample space. Write a probability problem that can be represented by the sample space. Then write the answer(s) to the problem.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-22.png\")
\nAnswer:<\/p>\nMaintaining Mathematical Proficiency<\/p>\n
Simplify the expression. Write your answer using only positive exponents.<\/p>\n
Question 29.
\n\\(\\frac{2 x^{3}}{x^{2}}\\)
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-29.png\")
<\/p>\nQuestion 30.
\n\\(\\frac{2 x y}{8 y^{2}}\\)
\nAnswer:
\n\\(\\frac{2y}{8 y^{2}}\\)
\n= \\(\\frac{2}{8y}\\)
\n= \\(\\frac{1}{4y}\\)<\/p>\nQuestion 31.
\n\\(\\frac{4 x^{9} y}{3 x^{3} y}\\)
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-31.png\")
<\/p>\nQuestion 32.
\n\\(\\frac{6 y^{0}}{3 x^{-6}}\\)
\nAnswer:
\nGiven,
\n\\(\\frac{6 y^{0}}{3 x^{-6}}\\)
\n= 6 . 1\/3x-6<\/sup>
\n= 2 . x6<\/sup><\/p>\nQuestion 33.
\n(3Pq)4<\/sup>
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.1-Qu-33.png\")
<\/p>\nQuestion 34.
\n\\(\\left(\\frac{y^{2}}{x}\\right)^{-2}\\)
\nAnswer: (\\(\\frac{y}{x}\\))\u00b2<\/p>\n<\/a>12.2 Independent and Dependent Events<\/h3>\n
Exploration 1<\/strong><\/p>\n
Identifying Independent and Dependent Events<\/p>\n
Work with a partner: Determine whether the events are independent or dependent. Explain your reasoning.
\nREASONING ABSTRACTLY<\/strong>
\nTo be proficient in math, you need to make sense of quantities and their relationships in problem situations.
\na. Two six-sided dice are rolled.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-23.png\")
\nAnswer:
\nP = Number of outcomes that satisfy the requirements\/Total number of possible outcomes
\nProbability for rolling two dice with the six sided dots such as 1, 2, 3, 4, 5 and 6 dots in each die.
\nWhen two dice are thrown simultaneously, thus the number of event can be 62 = 36 because each die has 1 to 6 number on its faces.
\nThis is independent event<\/p>\nb. Six pieces of paper, numbered 1 through 6, are in a bag, Two pieces of paper are selected one at a time without replacement.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-24.png\")
\nAnswer:
\nP = Number of outcomes that satisfy the requirements\/Total number of possible outcomes
\nWhen we pick up any paper the probability result is equal of 1\/6
\nThis is dependent event<\/p>\nExploration 2<\/strong><\/p>\n
Work with a partner:<\/p>\n
a. In Exploration 1(a), experimentally estimate the probability that the sum of the two numbers rolled is 7. Describe your experiment.
\nAnswer:<\/p>\n(b). In Exploration 1 (b), experimentally estimate the probability that the sum of the two numbers selected is 7. Describe your experiment.
\nAnswer:<\/p>\nExploration 3<\/strong><\/p>\n
Finding Theoretical Probabilities<\/p>\n
Work with a partner:
\na. In Exploration 1(a), find the theoretical probability that the sum of the two numbers rolled is 7. Then compare your answer with the experimental probability you found in Exploration 2(a).
\nAnswer:
\nFor each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6\/36 = 1\/6.<\/p>\nb. In Exploration 1(b). find the theoretical probability that the sum of the two numbers selected is 7. Then compare your answer with the experimental probability you found in Exploration 2(b).
\nAnswer:<\/p>\nC. Compare the probabilities you obtained in parts (a) and (b).
\nAnswer:<\/p>\nCommunicate Your Answer<\/p>\n
Question 4.
\nHow can you determine whether two events are independent or dependent?
\nAnswer:
\nTwo events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
\nIf whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.<\/p>\nQuestion 5.
\nDetermine whether the events are independent or dependent. Explain your reasoning.
\na. You roil a 4 on a six-sided die and spin red on a spinner.
\nAnswer: Independent<\/p>\nb. Your teacher chooses a student to lead a group. chooses another student to lead a second group. and chooses a third student to lead a third group.
\nAnswer: Dependent<\/p>\n<\/a>Lesson 12.2 Independent and Dependent Events<\/h3>\n
Monitoring progress<\/strong><\/p>\n
Question 1.
\nIn Example 1, determine whether guessing Question 1 incorrectly and guessing Question 2 correctly are independent events.
\nAnswer:<\/p>\nQuestion 2.
\nIn Example 2, determine whether randomly selecting a girl first and randomly selecting a boy second are independent events.
\nAnswer:<\/p>\nQuestion 3.
\nIn Example 3, what is the probability that you spin an even number and then an odd number?
\nAnswer:<\/p>\nQuestion 4.
\nIn Example 4, what is the probability that both hills are $1 hills?
\nAnswer:<\/p>\nQuestion 5.
\nIn Example 5, what is the probability that none of the cards drawn are hearts when (a) you replace each card, and (b) you do not replace each card? Compare the probabilities.
\nAnswer:
\n(a) you replace each card,
\nP(A and B and C) = P(A) P(B) P(C)
\n= 13\/52 . 13\/52 . 13\/52 = 1\/4 . 1\/4 . 1\/4 = 1\/64 = 0.016<\/p>\nQuestion 6.
\nIn Example 6, find (a) the probability that a non-defective part \u201cpasses\u201d and (b) the probability that a defective part “fails.”
\nAnswer:
\n(a) the probability that a non-defective part \u201cpasses\u201d
\nP(P\/D) = 3\/39 = 1\/13 = 0.077
\n(b) the probability that a defective part “fails.”
\nP(F\/N) = 11\/461 = 0.024<\/p>\nQuestion 7.
\nAt a coffee shop. 80% of customers order coffee. Only 15% of customers order coffee and a bagel. What is the probability that a customer who orders coffee also orders a bagel?
\nAnswer:
\nA: Customer order coffee
\nB: Customer order a bagel
\nP(B\/A) = P(A and B)\/P(A)
\n80% of customers order coffee and Only 15% of customers order coffee and a bagel.
\nP(A) = 80\/100 = 0.8
\nP(A and B) = 15\/100 = 0.15
\nP(B\/A) = P(A and B)\/P(A) = 0.15\/0.8 = 0.1875 = 18.75%<\/p>\n<\/a>Exercise 12.2 Independent and Dependent Events<\/h3>\n
Vocabulary and Core Concept Check<\/p>\n
Question 1.
\nWRITING<\/strong>
\nExplain the difference between dependent events and independent events, and give an example of each.
\nAnswer:
\nWhen two events are dependent, the occurrence of one event affects the other. When two events are independent, the occurence of one event does not affect the other.<\/p>\nQuestion 2.
\nCOMPLETE THE SENTENCE<\/strong>
\nThe probability that event B will occur given that event A has occurred is called the _____________ of B given A and is written as _____________ .
\nAnswer:
\nThe probability that event B will occur given that event A has occurred is called the conditional probability of B given A and is written as P(B\/A).<\/p>\nMonitoring Progress and Modeling with Mathematics<\/p>\n
In Exercises 3 – 6, tell whether the events are independent or dependent. Explain your reasoning.<\/p>\n
Question 3.
\nA box of granola bars contains an assortment of flavors. You randomly choose a granola bar and eat it. Then you randomly choose another bar.
\nEvent A: You choose a coconut almond bar first.
\nEvent B: You choose a cranberry almond bar second.
\nAnswer:
\nThe two events, which considered in this experiment are an example of dependent events.<\/p>\nQuestion 4.
\nYou roll a six-sided die and flip a coin.
\nEvent A: You get a 4 when rolling the die.
\nEvent B: You get tails when flipping the coin
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-25.png\")
\nAnswer: Independent, the events do not influence each other.<\/p>\nQuestion 5.
\nYour MP3 player contains hip-hop and rock songs. You randomly choose a song. Then you randomly choose another song without repeating song choices.
\nEvent A: You choose a hip-hop song first.
\nEvent B: You choose a rock song second.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-26.png\")
\nAnswer:
\nThe events are dependent because the occurrence of event A affects the occurrence of event B.<\/p>\nQuestion 6.
\nThere are 22 novels of various genres on a shell. You randomly choose a novel and put it back. Then you randomly choose another novel.
\nEvent A: You choose a mystery novel.
\nEvent B: You choose a science fiction novel.
\nAnswer:
\nThe 1st book chosen is put back so the second book picked has the same probability of being chosen a if the 1st book was never chosen to begin with the events are independent.<\/p>\nIn Exercises 7 – 10. determine whether the events are independent.<\/p>\n
Question 7.
\nYou play a game that involves spinning a wheel. Each section of the wheel shown has the same area. Use a sample space to determine whether randomly spinning blue and then green are independent events.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-27.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-7.png\")
<\/p>\nQuestion 8.
\nYou have one red apple and three green apples in a bowl. You randomly select one apple to eat now and another apple for your lunch. Use a sample space to determine whether randomly selecting a green apple first and randomly selecting a green apple second are independent events.
\nAnswer:
\nLet R represent the red apple.
\nLet G1, G2, G3 represent the 3 green apples.
\nP(G first) = P(green apple first) = 9\/12 = 3\/4 = 0.75
\nP(G second) = P(green apple second) = 9\/12 = 3\/4 = 0.75
\nP(green apple first and second) = 6\/12 = 1\/2 = 0.5
\nEvents are not independent.<\/p>\nQuestion 9.
\nA student is taking a multiple-choice test where each question has four choices. The student randomly guesses the answers to the five-question test. Use a sample space to determine whether guessing Question 1 correctly and Question 2 correctly are independent events.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-9.png\")
<\/p>\nQuestion 10.
\nA vase contains four white roses and one red rose. You randomly select two roses to take home. Use a sample space to determine whether randomly selecting a white rose first and randomly selecting a white rose second are independent events.
\nAnswer:
\nP(A and B) = P(A) and P(B)
\nA = {First randomly selected roses is white}
\nB = {Second randomly selected roses is white}
\nP(A) = Number of favorable outcomes\/Total number of outcomes = 4\/5
\nP(B) = 4\/5
\nP(A) . P(B) = 4\/5 . 4\/5 = 16\/25<\/p>\nQuestion 11.
\nPROBLEM SOLVING<\/strong>
\nYou play a game that involves spinning the money wheel shown. You spin the wheel twice. Find the probability that you get more than $500 on your first spin and then go bankrupt on your second spin.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-28-1.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-11.png\")
<\/p>\nQuestion 12.
\nPROBLEM SOLVING<\/strong>
\nYou play a game that involves drawing two numbers from a hat. There are 25 pieces of paper numbered from 1 to 25 in the hat. Each number is replaced after it is drawn. Find the probability that you will draw the 3 on your first draw and a number greater than 10 on your second draw.
\nAnswer:
\nP(A) = 1\/25
\nP(B) = 15\/25
\nP(A and B) = P(A) . P(B)
\n= 1\/25 . 15\/25 = 3\/125
\nThus P(A and B) = 3\/125<\/p>\nQuestion 13.
\nPROBLEM SOLVING<\/strong>
\nA drawer contains 12 white socks and 8 black socks. You randomly choose 1 sock and do not replace it. Then you randomly choose another sock. Find the probability that both events A and B will occur.
\nEvent A: The first sock is white.
\nEvent B: The second sock is white.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-13.png\")
<\/p>\nQuestion 14.
\nPROBLEM SOLVING<\/strong>
\nA word game has 100 tiles. 98 of which are letters and 2 of which are blank. The numbers of tiles of each letter are shown. You randomly draw 1 tile, set it aside, and then randomly draw another tile. Find the probability that both events A and B will occur.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-29.png\")
\nAnswer:
\nP(A) = 56\/100 = 0.56
\nP(B) = 42\/(100 – 1) = 0.424
\nP(A) . P(B) = 0.56 \u00d7 0.424 = 0.2376<\/p>\nQuestion 15.
\nERROR ANALYSIS<\/strong>
\nEvents A and B are independent. Describe and correct the error in finding P(A and B).
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-30.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-15.png\")
<\/p>\nQuestion 16.
\nERROR ANALYSIS<\/strong>
\nA shelf contains 3 fashion magazines and 4 health magazines. You randomly choose one to read, set it aside, and randomly choose another for your friend to read. Describe and correct the error in finding the probability that both events A and B occur.
\nEvent A: The first magazine is fashion.
\nEvent B: The second magazine is health.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-31.png\")
\nAnswer:
\nP(A) = 3\/7
\nP(B\/A) = 4\/(7 – 1) = 4\/6
\nP(A and B) = P(A) \u00d7 P(B\/A)
\nP(A and B) = 3\/7 \u00d7 4\/6 = 2\/7<\/p>\nQuestion 17.
\nNUMBER SENSE<\/strong>
\nEvents A and B are independent. Suppose P(B) = 0.4 and P(A and B) = 0.13. Find P(A).
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-17.png\")
<\/p>\nQuestion 18.
\nNUMBER SENSE<\/strong>
\nEvents A and B are dependent. Suppose P(B\/A) = 0.6 and P(A and B) = 0.15. Find P(A).
\nAnswer:
\nP(A) = x
\nP(B\/A) = 0.6
\nP(A and B) = 0.15
\nP(A and B) = P(A) \u00d7 P(B\/A)
\n0.15 = x \u00d7 0.6
\nx = 0.15\/0.6
\nx = 0.25<\/p>\nQuestion 19.
\nANALYZING RELATIONSHIPS<\/strong>
\nYou randomly select three cards from a standard deck of 52 playing cards. What is the probability that all three cards are face cards when (a) you replace each card before selecting the next card, and (b) you do not replace each card before selecting the next card? Compare the probabilities.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-19.png\")
<\/p>\nQuestion 20.
\nA bag contains 9 red marbles. 4 blue marbles, and 7 yellow marbles. You randomly select three marbles from the hag. what is the probability that all three marbles are red when (a) you replace each marble before selecting the next marble, and (b) you do not replace each marble before selecting the next marble? Compare the probabilities.
\nAnswer:
\na. There are a total of 9 + 4 + 7= 20 marbles.
\nTherefore, the probability of selecting a red marble in each attempt is 9\/20 when the marble is replaced.
\nTherefore the probability of selecting a red marble in each of 3 of the attempt is
\n9\/20 \u00d7 9\/20 \u00d7 9\/20 = 0.09125
\nThe replacement makes these independent events.
\nb. There are total of 9 + 4 + 7 = 20 marbles.
\nThe probability of selecting a red marble in the first attempt is 9\/20, second attempt is 8\/19 and the third attempt is 7\/18 when the marbles are not replaced.
\nTherefore the probability of selecting a red marble in each of 3 of the attempts is 9\/20 \u00d7 8\/19 \u00d7 7\/18 = 0.0737<\/p>\nQuestion 21.
\nATTEND TO PRECISION<\/strong>
\nThe table shows the number of species in the United States listed as endangered and threatened. Find (a) the probability that a randomly selected endangered species is a bird, and (b) the probability that a randomly selected mammal is endangered.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-32.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-21.png\")
<\/p>\nQuestion 22.
\nATTEND TO PRECISION<\/strong>
\nThe table shows the number of tropical cyclones that formed during the hurricane seasons over a 12-year period. Find (a) the probability to predict whether a Future tropical cyclone in the Northern Hemisphere is a hurricane, and (b) the probability to predict whether a hurricane is in the Southern Hemisphere.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-33.png\")
\nAnswer:<\/p>\nQuestion 23.
\nPROBLEM SOLVING<\/strong>
\nAt a school, 43% of students attend the homecoming football game. Only 23% of students go to the game and the homecoming dance. What is the probability that a student who attends the football game also attends the dance?
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-23.png\")
<\/p>\nQuestion 24.
\nPROBLEM SOLVING<\/strong>
\nAt a gas station. 84% of customers buy gasoline. Only 5% of customers buy gasoline and a beverage. What is the probability that a customer who buys gasoline also buys a beverage?
\nAnswer:
\nGiven,
\nP(A) = 84% = 0.84
\nP(A and B) = 5% = 0.05
\nP(A and B) = P(A) \u00d7 P(B\/A)
\nP(B\/A) = 0.05\/0.84
\nP(B\/A) = 0.0595<\/p>\nQuestion 25.
\nPROBLEM SOLVING<\/strong>
\nYou and 19 other students volunteer to present the \u201cBest Teacher\u201d award at a school banquet. One student volunteer will be chosen to present the award. Each student worked at least 1 hour in preparation for the banquet. You worked for 4 hours, and the group worked a combined total of 45 hours. For each situation, describe a process that gives you a \u201cfair\u201d chance to be chosen. and find the probability that you are chosen.
\na. \u201cFair\u201d means equally likely.
\nb. \u201cFair\u201d means proportional to the number of hours each student worked in preparation.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-25.png\")
<\/p>\nQuestion 26.
\nHOW DO YOU SEE IT?<\/strong>
\nA bag contains one red marble and one blue marble. The diagrams show the possible outcomes of randomly choosing two marbles using different methods. For each method. determine whether the marbles were selected with or without replacement.
\na.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-34.png\")
\nAnswer:<\/p>\nb.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-35.png\")
\nAnswer:<\/p>\nQuestion 27.
\nMAKING AN ARGUMENT<\/strong>
\nA meteorologist claims that there is a 70% chance of rain. When it rains. there is a 75% chance that your softball game will be rescheduled. Your friend believes the game is more likely to be rescheduled than played. Is your friend correct? Explain your reasoning.
\nAnswer:
\nThe chance that the game will be rescheduled is (0.7)(0.75) = 0.525
\nwhich is 52.5 percent
\nmaking it greater than 50 percent.<\/p>\nQuestion 28.
\nTHOUGHT PROVOKING<\/strong>
\nTwo six-sided dice are rolled once. Events A and B are represented by the diagram. Describe each event. Are the two events dependent or independent? Justify your reasoning.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-36.png\")
\nAnswer:<\/p>\nQuestion 29.
\nMODELING WITH MATHEMATICS<\/strong>
\nA football team is losing by 14 points near the end of a game. The team scores two touchdowns (worth 6 points each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick (which is successful 99% of the time) or 2 points with a run or pass (which is successful 45% of the time).
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-37.png\")
\na. If the team goes for 1 point after each touchdown, what is the probability that the team wins? loses? ties?
\nb. If the team goes for 2 points after each touchdown. what is the probability that the team wins? loses? ties?
\nc. Can you develop a strategy so that the coach\u2019s team has a probability of winning the game that is greater than the probability of losing? If so, explain your strategy and calculate the probabilities of winning and losing the game.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-29.png\")
<\/p>\nQuestion 30.
\nABSTRACT REASONING<\/strong>
\nAssume that A and B are independent events.
\na. Explain why P(B) = P(B\/A) and P(A) = P(A\/B).
\nAnswer:
\nP(B) = P(B\/A)
\nP(B) = P(A) . P(B\/A)
\nP(A) = P(A\/B).
\nP(A) = P(B) . P(A\/B)<\/p>\nb. Can P(A and B) also be defined as P(B) \u2022 P(A\/B)? Justify your reasoning.
\nAnswer:<\/p>\nMaintaining Mathematical Proficiency<\/p>\n
Solve the equation. Check your solution.<\/p>\n
Question 31.
\n\\(\\frac{9}{10}\\) x = 0.18
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-31.png\")
<\/p>\nQuestion 32.
\n\\(\\frac{1}{4}\\)x + 0.5x = 1.5
\nAnswer:
\nGiven,
\n\\(\\frac{1}{4}\\)x + 0.5x = 1.5
\n0.25x + 0.50x = 1.5
\n0.75x = 1.5
\nx = 1.5\/0.75
\nx = 2<\/p>\nQuestion 33.
\n0.3x – \\(\\frac{3}{5}\\)x + 1.6 = 1.555
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.2-Qu-33.png\")
<\/p>\n<\/a>12.3 Two-Way Tables and Probability<\/h3>\n
Exploration 1<\/strong><\/p>\n
Completing and Using a Two-Way Table<\/p>\n
Work with a partner: A two-way table displays the same information as a Venn diagram. In a two-way table, one category is represented by the rows and the other category is represented by the columns.<\/p>\n
The Venn diagram shows the results of a survey in which 80 students were asked whether they play a musical instrument and whether they speak a foreign language. Use the Venn diagram to complete the two-way table. Then use the two-way table to answer each question.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-38.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-39.png\")
\na. How many students play an instrument?
\nAnswer: 41<\/p>\nb. How many students speak a foreign language?
\nAnswer: 46<\/p>\nc. How many students play an instrument and speak a foreign language?
\nAnswer: 16<\/p>\nd. How many students do not play an instrument and do not speak a foreign language?
\nAnswer: 9<\/p>\ne. How many students play an instrument and do not speak a foreign language?
\nAnswer: 25<\/p>\nExploration 2<\/strong><\/p>\n
Two – Way Tables and Probability<\/p>\n
Work with a partner. In Exploration 1, one student is selected at random from the 80 students who took the survey. Find the probability that the student
\na. plays an instrument.
\nAnswer: 41\/80<\/p>\nb. speaks a foreign language.
\nAnswer: 46\/80<\/p>\nc. plays an instrument and speaks a foreign language.
\nAnswer: 16\/80<\/p>\nd. does not play an instrument and does not speak a foreign language.
\nAnswer: 9\/80<\/p>\ne. plays an instrument and does not speak a foreign language.
\nAnswer:<\/p>\nExploration 3<\/strong><\/p>\n
Conducting a Survey<\/p>\n
Work with your class. Conduct a survey of the students in your class. Choose two categories that are different from those given in Explorations 1 and 2. Then summarize the results in both a Venn diagram and a two-way table. Discuss the results.
\nMODELING WITH MATHEMATICS<\/strong>
\nTo be proficient in math, you need to identify important quantities in a practical situation and map their relationships using such tools as diagrams and two-way tables.
\nAnswer:<\/p>\nCommunicate Your Answer<\/p>\n
Question 4.
\nHow can you construct and interpret a two-way table?
\nAnswer:
\nIdentify the variables. There are two variables of interest here: the commercial viewed and opinion.
\nDetermine the possible values of each variable. For the two variables, we can identify the following possible values
\nSet up the table
\nFill in the frequencies<\/p>\nQuestion 5.
\nHow can you use a two-way table to determine probabilities?
\nAnswer:<\/p>\n<\/a>Lesson 12.3 Two-Way Tables and Probability<\/h3>\n
Monitoring Progress<\/strong><\/p>\n
Question 1.
\nYou randomly survey students about whether they are in favor of planting a community garden at school. of 96 boys surveyed, 61 are in favor. 0f 88 girls surveyed, 17 are against. Organize the results in a two-way table. Then find and interpret the marginal frequencies.
\nAnswer:
\nIn order to find out how many boys are against you do 96 – 61. In order to find out how many girls are in favor you do 88 – 17.
\nIn order to find the probability you make a proportion. It will be:
\nP\/100 = number of girls against\/total number of students
\n17\/184 = p\/100
\n17 \u00d7 100 = 184p
\n1700 = 184p
\np = 9.23<\/p>\nQuestion 2.
\nUse the survey results in Monitoring Progress Question 1 to make a two-way table that shows the joint and marginal relative frequencies.
\nAnswer:<\/p>\nQuestion 3.
\nUse the survey results in Example 1 to make a two-way table that shows the conditional relative frequencies based on the column totals. Interpret the conditional relative frequencies in the context of the problem.
\nAnswer:<\/p>\nQuestion 4.
\nUse the survey results in Monitoring Progress Question 1 to make a two-way table that shows the conditional relative frequencies based on the row totals. Interpret the conditional relative frequencies in the context of the problem.
\nAnswer:<\/p>\nQuestion 5.
\nIn Example 4, what is the probability that a randomly selected customer who is located in Santa Monica will not recommend the provider to a friend?
\nAnswer:<\/p>\nQuestion 6.
\nIn Example 4, determine whether recommending the provider to a friend and living in Santa Monica are independent events. Explain your reasoning.
\nAnswer:<\/p>\nQuestion 7.
\nA manager is assessing three employees in order to offer one of them a promotion. Over a period of time, the manager records whether the employees meet or exceed expectations on their assigned tasks. The table shows the managers results. Which employee should be offered the promotion? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-40.png\")
\nAnswer:<\/p>\n<\/a>Exercise 12.3 Two-Way Tables and Probability<\/h3>\n
Vocabulary and Core Concept Check<\/p>\n
Question 1.
\nCOMPLETE THE SENTENCE<\/strong>
\nA(n) ______________ displays data collected from the same source that belongs to two different categories.
\nAnswer:
\nA two-way table displays data collected from the same source that belongs to two different categories.<\/p>\nQuestion 2.
\nWRITING
\nCompare the definitions of joint relative frequency, marginal relative frequency, and conditional relative frequency.
\nAnswer:
\nJoint relative frequency: joint relative frequency is the ratio of a frequency that is not in the total row or the total column to the total number of values.
\nMarginal relative frequency: marginal relative frequency is the sum of the joint relative frequencies in a given row or column.
\nConditional relative frequency: It is the ratio of joint relative frequency to the marginal relative frequency.<\/p>\nMonitoring Progress and Modeling with Mathematics<\/p>\n
In Exercises 3 and 4, complete the two-way table.<\/p>\n
Question 3.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-41.png\")
\nAnswer:
\nNumber of students who have passed the exam is 50 – 10 = 40
\nOf those 40 students, 6 did not study for the exam,
\nNumber of the students who studied and have passed the exam is 40 – 6 = 34
\nNumber of the students who did not study and did not pass the exam is 10 – 4 = 6
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-3.png\")
<\/p>\nQuestion 4.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-42.png\")
\nAnswer:
\nNumber of students who said no is 49 – 7 = 42
\nTotal number of students is 56 + 42 = 98
\nTotal number of people is 98 + 10 = 108
\nOut of the total number of people, 49 of them said no,
\nTotal number of people who said yes is 108 – 49 = 59
\nNumber of teachers who said yes is 59 – 56 = 3
\n![\"Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-42](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-42-1-300x115.png\")
<\/p>\nQuestion 5.
\nMODELING WITH MATHEMATICS<\/strong>
\nYou survey 171 males and 180 females at Grand Central Station in New York City. Of those, 132 males and 151 females wash their hands after using the public rest rooms. Organize these results in a two-way table. Then find and interpret the marginal frequencies.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-43.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-5.1.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-5.2.png\")
<\/p>\nQuestion 6.
\nMODELING WITH MATHEMATICS<\/strong>
\nA survey asks 60 teachers and 48 parents whether school uniforms reduce distractions in school. Of those, 49 teachers and 18 parents say uniforms reduce distractions in school, Organize these results in a two-way table. Then find and interpret the marginal frequencies.
\nAnswer:
\nGiven,
\nA survey asks 60 teachers and 48 parents whether school uniforms reduce distractions in school. Of those, 49 teachers and 18 parents say uniforms reduce distractions in school
\nNumber of teacher who said no is 60 – 49 = 11
\nNumber of parents who said no = 48 – 18 = 30
\nTotal number of people who said yes = 49 + 18 = 67
\nTotal number of people who said no = 11 + 30 = 41
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Big-Ideas-Math-Answers-Geometry-Chapter-12-Probability-img_15-300x93.png\")
<\/p>\nUSING STRUCTURE<\/strong>
\nIn Exercises 7 and 8, use the two-way table to create a two-way table that shows the joint and marginal relative frequencies.<\/p>\nQuestion 7.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-44.png\")
\nAnswer:
\nP1,1 <\/sub>= Number of favorable outcomes\/Total number of outcomes
\n= 11\/231 = 0.0476
\nP2,1 <\/sub>= 24\/231 = 0.1039
\nP1,2 <\/sub>= 104\/231 = 0.4502
\nP2,2 <\/sub>= 92\/231 = 0.3983
\nThe marginal relative frequencies we find as the sum of each row and each column.
\nP(A randomly chosen person is male) = 115\/231 = 0.4978
\nP(A randomly chosen person is female) = 116\/231 = 0.5022
\nP(A randomly chosen person have left dominant hand) = 35\/231 = 0.1515
\nP(A randomly chosen person have left dominant hand) = 196\/231 = 0.8484
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-7.png\")
<\/p>\nQuestion 8.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-45.png\")
\nAnswer:
\nP1,1 <\/sub>= Number of favorable outcomes\/Total number of outcomes
\n= 62\/410 = 0.1513
\nThe marginal relative frequencies we find as the sum of each row and each column.
\nP(A randomly chosen person is male) = 377\/410 = 0.9195
\nP(A randomly chosen person is female) = 33\/410 = 0.0805<\/p>\nQuestion 9.
\nMODELING WITH MATHEMATICS<\/strong>
\nUse the survey results from Exercise 5 to make a two-way table that shows the joint and marginal relative frequencies.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-9.png\")
<\/p>\nQuestion 10.
\nMODELING WITH MATHEMATICS<\/strong>
\nIn a survey, 49 people received a flu vaccine before the flu season and 63 people did not receive the vaccine. Of those who receive the flu vaccine, 16 people got the flu. Of those who did not receive the vaccine, 17 got the flu. Make a two-way table that shows the joint and marginal relative frequencies.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-46.png\")
\nAnswer:
\nWe see that the total no. of people who received the vaccine is 49, of which 16 got a fly.
\nNumber of people who received the vaccine and did not get a fly is 49 – 16 = 33
\nNumber of people who did not received the vaccine and did not get a fly is 63 – 17 = 46
\nTotal number of people who got a fly is 16 + 17 = 33
\nTotal Number of people who did not get a fly is 33 + 46 = 79
\nWe also know that the total number of people who were surveyed is 49 + 63 = 112
\nP1,1 <\/sub>= Number of favorable outcomes\/Total number of outcomes
\n= 16\/112 = 0.1428
\nThe marginal relative frequencies we find as the sum of each row and each column.
\nP(A randomly chosen person got a fly) = 33\/112 = 0.2946
\nP(A randomly chosen person did not get a fly) = 79\/112 = 0.7053<\/p>\nQuestion 11.
\nMODELING WITH MATHEMATICS<\/strong>
\nA survey finds that 110 people ate breakfast and 30 people skipped breakfast. Of those who ate breakfast. 10 people felt tired. Of those who skipped breakfast. 10 people felt tired. Make a two-way table that shows the conditional relative frequencies based on the breakfast totals.
\nAnswer:
\nGiven,
\nA survey finds that 110 people ate breakfast and 30 people skipped breakfast.
\nOf those who ate breakfast. 10 people felt tired. Of those who skipped breakfast. 10 people felt tired.
\nNumber of people who ate breakfast and not tired is 110 – 10 = 100
\nNumber of people who did not eat breakfast and not tired is 30 – 10 = 20
\nTotal number of people who felt tired is 10 + 10 = 20
\nTotal number of people who did not get tired is 100 + 20 = 120
\n120 +20 = 140
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-11.png\")
<\/p>\nQuestion 12.
\nMODELING WITH MATHEMATICS<\/strong>
\nUse the survey results from Exercise 10 to make a two-way table that shows the conditional relative frequencies based on the flu vaccine totals.
\nAnswer:<\/p>\nQuestion 13.
\nPROBLEM SOLVING<\/strong>
\nThree different local hospitals in New York surveyed their patients. The survey asked whether the patients physician communicated efficiently. The results, given as joint relative frequencies. are shown in the two-way table.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-47.png\")
\na. What is the probability that a randomly selected patient located in Saratoga was satisfied with the communication of the physician?
\nb. What is the probability that a randomly selected patient who was not satisfied with the physician\u2019s communication is located in Glens Falls?
\nc. Determine whether being satisfied with the Communication of the physician and living in Saratoga are independent events.
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-13.png\")
<\/p>\nQuestion 14.
\nPROBLEM SOLVING<\/strong>
\nA researcher surveys a random sample of high school students in seven states. The survey asks whether students plan to stay in their home state after graduation. The results, given as joint relative frequencies, are shown in the two-way table.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-48.png\")
\na. What is the probability that a randomly selected student who lives in Nebraska plans to stay in his or her home state after graduation?
\nAnswer:
\nIn this case we consider a event A = {arandomly chosen student lives in Nebraska}
\nB = {a randomly chosen student plans to stay in his or her home state after graduation}
\nP(A) = 0.044 + 0.4 = 0.444
\nP(B\/A) = P(A and B)\/P(A) = 0.044\/0.444 = 0.099
\nAbout 1% students who lives Nebraska plans to stay in his or her home state after graduation.<\/p>\nb. What is the probability that a randomly selected student who does not plan to stay in his or her home state after graduation lives in North Carolina?
\nAnswer:
\nC = {a randomly chosen student does not plan to stay in his or her home state after graduation}
\nD = {a randomly chosen student lives in North Carolina}
\nP(C) = 0.4 + 0.193 + 0.256 = 0.849
\nP(D\/C) = P(C and D)\/P(C)
\n= 0.193\/0.849 = 0.227
\nTherefore about 22.7% students who does not plan to stay in his or her home state after graduation lives in North Carolina.<\/p>\nc. Determine whether planning to stay in their home state and living in Nebraska are independent events.
\nAnswer:
\nP(B\/A) = 0.099
\nP(B) = 0.044 + 0.05
\n1 + 0.056 = 0.151
\nP(B\/A) \u2260 P(B)
\nThis events are independent.<\/p>\nERROR ANALYSIS<\/strong>
\nIn Exercises 15 and 16, describe and correct the error in finding the given conditional probability.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-49.png\")
<\/p>\nQuestion 15.
\nP(yes|Tokyo)
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-50.png\")
\nAnswer:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-12-Probability-12.3-Qu-15.png\")
<\/p>\nQuestion 16.
\nP(London|No)
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-12-Probability-51.png\")
\nAnswer:
\nP(A and B) = P(A)P(B\/A)
\nP(A) = 0.341 + 0.112+ 0.191 = 0.644
\nP(B\/A) = P(A and B)\/P(A) = 0.112\/0.644 = 0.1739
\nIn the denominator the probability P(B) = 0.248 is used instead of P(A), where P(B) is probability that a randomly chosen person live in London.<\/p>\nQuestion 17.
\nPROBLEM SOLVING<\/strong> - Probability Test<\/a><\/li>\n
- Lesson 12.6 Binomial Distributions<\/a><\/li>\n
- Lesson 12.5 Permutations and Combinations<\/a><\/li>\n
- Lesson 12.4 Probability of Disjoint and Overlapping Events<\/a><\/li>\n
- 12.4 Probability of Disjoint and Overlapping Events<\/a><\/li>\n
- Lesson 12.3 Two-Way Tables and Probability<\/a><\/li>\n
- Lesson 12.2 Independent and Dependent Events<\/a><\/li>\n
- Lesson 12.1 Sample Spaces and Probability<\/a><\/li>\n
- Probability Monitoring Progress<\/a><\/li>\n<\/ul>\n