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# MATH 225N Week 4 Homework Assignment: Probability Questions & Answers 2020/2021

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1. Which of the pairs of events below is dependent? Select the correct answer below:
2. Question: Identify the option below that represents dependent events. Select the correct answer below:
3. Question: … shows mutually exclusive events? Select the correct answer below:
4. Question: Which of the pairs of events below is mutually exclusive? Select the correct answer below:
5. Question: A deck of cards contains RED cards numbered 1,2,3,4,5,6, BLUE cards numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is … at random, what is the probability that the card has an ODD number?
6. Question: Hector is a baseball fan but wants to watch something different. There are 5basketball games, 2 football games, and 4hockey games that he can choose to watch. If Hector randomly chooses a game, what is the probability that it is a basketball game?
7. Question: There are 26cards in a hat, each of them containing a different letter of the alphabet. If one card is … at random, what is the probability that it is not between the letters L and P, inclusive?
8. Question: A spinner contains the numbers 1through 80. What is the probability that the spinner will land on a number that is not a multiple of 12?
9. Question: An art collector wants to purchase a new piece of art. She is … in 5paintings, 6 vases, and 2 If she … the piece at random, what is the probability that she … a painting?
10. Question: Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2high-difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is the probability that Boris is assigned a moderate-difficulty question first?
11. Question: A spinner contains the numbers 1through 40. What is the probability that the spinner will land on a number that is not a multiple of 6? Give your answer as a fraction.
12. Question: A spinner contains the numbers 1through 50. What is the probability that the spinner will land on a number that is not a multiple of 4?
13. Question: Identify the parameters pand n in the following binomial distribution scenario. The probability of winning an arcade game is 718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)
14. Question: A weighted coin has a 55probability of landing on heads. If you toss the coin 14 times, what is the probability of getting heads exactly 9 times? (Round your answer to 3 decimal places if necessary.)
15. Question: Identify the parameter pin the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 546 and without a popcorn coupon is 0.454. If you buy 27 movie tickets, we want to know the probability that exactly 15 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)
16. Question: A softball pitcher has a 64probability of throwing a strike for each pitch. If the softball pitcher throws 20 pitches, what is the probability that exactly 13 of them are strikes?
17. Question: Identify the parameter nin the following binomial distribution scenario. A basketball player has a 429 probability of making a free throw and a 0.571 probability of missing. If the player shoots 20 free throws, we want to know the probability that he makes no more than 12 of them. (Consider made free throws as successes in the binomial distribution.)
18. Question: Give the numerical value of the parameter pin the following binomial distribution scenario…..A softball pitcher has a 675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes……..Consider strikes as successes in the binomial distribution. Do not include p= in your answer.
19. Question: Identify the parameters pand n in the following binomial distribution scenario……Jack, a bowler, has a 38 probability of throwing a strike and a 0.62 probability of not throwing a strike. Jack bowls 20times (Consider that throwing a strike is a success.)…….The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6matches. What is the mean for the number of matches that they win in the tournament?
20. Question: Using the same scenario, what is the standard deviation for the number of matches that they win in the tournament?
21. Question: The Stomping Elephants volleyball team plays 30matches in a week-long tournament. On average, they win 4 out of every 6
22. Question: Identify the parameter nin the following binomial distribution scenario. A weighted coin has a 441 probability of landing on heads and a 0.559 probability of landing on tails. If you toss the coin 19 times, we want to know the probability of getting heads more than 5 times. (Consider a toss of heads as success in the binomial distribution.)
23. Question: Give the numerical value of the parameter n, the number of trials, in the following binomial distribution scenario.
A weighted coin has a 486probability of landing on heads and a 0.514 probability of landing on tails. If you toss the coin 27 times, we want to know the probability of getting heads exactly 11 times.
Consider a toss of heads as success in the binomial distribution.
24. Question: The probability of winning on an arcade game is 659. If you play the arcade game 30times, what is the probability of winning exactly 21 times?
25. Question: The probability of buying a movie ticket with a popcorn coupon is 526. If you buy 26movie tickets, what is the probability that exactly 15 of the tickets have popcorn coupons?
26. Question: The probability of buying a movie ticket with a popcorn coupon is 608. If you buy 10movie tickets, what is the probability that more than 3 of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)
27. Question: A softball pitcher has a 507probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes? (Round your answer to 3 decimal places if necessary.)
28. Question: A 2014 study by researchers at the University College Antwerp and the University of Leuven showed that e-cigarettes are effective at reducing cigarette craving.  Participants were separated into two groups. One group was … e-cigarettes and the other was told to not smoke e-cigarettes. Two months later, researchers observed how many participants had stopped smoking cigarettes……..The following table shows approximate numbers. According to the table, what is the probability that a randomly … participant did not stop smoking, … that the participant received an e-cigarette?
29. Question: Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 The data are … in the contingency table below. What is the relative risk of flying for those birds that have long beaks? … decimal places.
30. Question: Given the contingency table below, determine the marginal distribution of breakfast and lunch. Round your answer(s) to the nearest whole number. Select all that apply.
31. Question: 155fitness center members were asked if they run and if they lift weights. The results are … in the table below……. Given that a randomly selected survey participant does not run, what is the probability that the participant lifts weights?
32. Question: Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
33. Question: Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 The data are … in the contingency table below. What is the odds ratio for birds that fly having long beaks against birds that do not fly having long beaks? Round your answer to two decimal places…….. Fill in the following contingency table and find the number of students who both watch comedies AND watch dramas.
34. Question: Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for married people having children against unmarried people having children? Round your answer to two decimal places.
35. Question: Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are … in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.
36. Question: A group of college freshman are targeted with a voter registration advertisement. Another group of freshman are not targeted. The table below shows how many of these freshman registered to vote. What is the odds ratio for freshman targeted with the advertisement registering to vote against freshman not targeted with the advertisement registering to vote? Does the advertisement appear to have been successful? Round to two decimal places.
37. Question: Researchers … to depression. They surveyed a large group of people. The data are … in the contingency table below. What is the relative risk of … ? Round your answer to two decimal places.
38. Question: Researchers want to study whether or not a fear of flying is related to a fear of heights. They surveyed a large group of people and asked them whether or not they had a fear of flying and whether or not they had a fear of heights. The data are … in the contingency table below. What is the relative risk of being afraid of flying for those who are afraid of heights? Round your answer to two decimal places.
39. Question: A study of drivers with speeding violations in the last year and drivers who use cell phones produced the following fictional data: ………. Find the probability that a randomly chosen person takes public transit to work given that the person does not support the environmental bill.
40. Question: Fill in the following contingency table and find the number of students who both do not go to the beach AND do not go to the mountains.
41. Question: Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
42. Question: Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for people having children to … married against people not having children to … married? Round your answer to two decimal places.
43. Question: Researchers wanted to study if wearing cotton clothes is related to depression. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for people wearing cotton clothes being depressed against people not wearing cotton clothes … depressed? Round your answer to two decimal places.
44. Question: Review the flu vaccine data below. What is the odds ratio of not catching the flu for those who receive the new vaccine?
45. Question: Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are … in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.
46. Question: In a recent survey, a group of people were asked if they were happy or unhappy with the state of the country. The data are … in the contingency table below, organized by political party. What is the odds ratio for people unhappy with the state of the country to be republicans against people happy with the state of the country to … republicans? … two decimal places.
47. Question: Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the relative risk of being married for those who have children? Round your answer to two decimal places.
48. Question: Kelsey, a basketball player, hits 3-point shots on 1%of her attempts. If she takes 14 attempts at 3-point shots in a game, what is the probability that she hits exactly six of them? Use Excel to find the probability.
49. Question: A computer graphics card manufacturer is testing an improvement to its production process. If a sample of 100graphics cards manufactured using the new process has a less than 10% chance of having 3 or more defective graphics cards, then the manufacturer will switch to the new process. Otherwise, the manufacturer will stay with its existing process. If the probability of a defective graphics card using the new process is 9%, will the manufacturer switch to the new production process?
50. Question: In a large city’s recent mayoral election, 126,519out of 283,143 registered voters actually turned out to vote. If 20registered voters are randomly selected, find the probability that exactly 8 of them voted in the mayoral election. Use Excel to find the probability.
51. Question: Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 If there is more than a 50%chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.
52. Question: A certain cold remedy has an 88%rate of success of reducing symptoms within 24 Find the probability that in a random sample of 45 people who took the remedy, 40 of them had a reduction of symptoms within a day.
53. Question: Kevin works for a company that manufactures solar panels. In a large batch of solar panels, about 1in 200 is defective. Suppose that Kevin selects a random sample of six solar panels from this batch. What is the probability that none of the solar panels are defective? Use Excel to find the probability.
54. Question: A database system assigns a 32-character ID to each record, where each character is either a number from 0to 9 or a letter from A to F. Assume that each number or letter … is equally … Find the probability that at least 20characters in the ID are numbers. Use Excel to find the probability.
55. Question: A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an experiment, the spinner will … spun 5 If Event A = the spinner lands on numbers all less than 3, what is an outcome of Event A?
56. Question: A poll is conducted to determine if political party has any association with whether a person is for or against a certain bill. In the poll, 214out of 432 Democrats and 246 out of 421 Republicans are in favor of the bill. Assuming political party has no association, the probability of these results being by chance is calculated to … 01. Interpret the results of the calculation.
57. Question: Arianna will roll a standard die 10times in which she will record the value of each roll. What is a trial of this experiment?
58. Question: A health survey determined the mean weight of a sample of 762men between the ages of 26 and 31 to … 173 pounds, while the mean weight of a sample of 1,561 men between the ages of 67 and 72 was 162 The difference between the mean weights is significant at the 0.05 level. Determine the meaning of this significance level.
59. Question: The mean body temperature of a human is … 6∘F. In a study, the body temperatures of 127individuals were … The mean body temperature of the individuals was … 99.0∘F. Assuming the regular body temperature of humans is actually 98.6∘F, the probability of these results occurring by chance is less than 0.01. Interpret the results of the calculation.
60. Question: Which of the following events seem like they would … unlikely to occur by chance?
61. Question: Before a college professor gave an exam, he held a review session, where 30of his 150 students attended the review. The mean score of the students who attended was 86%, whereas the mean score of the students who didn’t attend the review was 79%. The difference in the mean scores is significant at the 05 level, assuming the review session does not associate with a higher exam score. Determine the meaning of this significance level.
62. Question: According to a recent poll, 5%of people aged 25 years or older in the state of Massachusetts have a bachelor’s degree or higher. The poll also reported that 30.0% of people aged 25 years or old
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