Download MATH 225N WEEK 4 PROBABILITY QUESTIONS AND ANSWERS 2022/2023 and more Exams Nursing in PDF only on Docsity!
1. Which of the pairs of events below is dependent?
Select the correct answer below:
drawing a 7 and then drawing another 7 with replacement from a standard deck of cards rolling a 1 and then rolling a 6 with a standard die rolling a 3 and then rolling a 4 with a standard die drawing a heart and then drawing a spade without replacement from a standard deck of cards
2. Identify the option below that represents dependent events.
Select the correct answer below:
drawing a face card and then drawing a 3 without replacement from a standard deck of cards rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two rolls drawing a 2 and drawing a 4 with replacement from a standard deck of cards drawing a heart and drawing another heart with replacement from a standard deck of cards
3. Which of the following shows mutually exclusive events?
Select the correct answer below:
rolling a sum of 9 from two rolls of a standard die and rolling 2 for the first roll drawing a red card and then drawing a black card with replacement from a standard deck of cards drawing a jack and then drawing a 7 without replacement from a standard deck of cards drawing a 7 and then drawing another 7 with replacement from a standard deck of cards
4. Which of the pairs of events below is mutually exclusive?
Select the correct answer below:
drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards
drawing a 2 and drawing a 4 with replacement from a standard deck of cards drawing a heart and then drawing a spade without replacement from a standard deck of cards drawing a jack and then drawing a 7 without replacement from a standard deck of cards
9. An art collector wants to purchase a new piece of art. She is interested in 5 paintings, 6 vases, and 2 statues. If she chooses the piece at random, what is the probability that she selects a painting?
- Give your answer as a fraction.
Provide your answer below: 5/
10. Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2 high- difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is the probability that Boris is assigned a moderate-difficulty question first?
- Give your answer as a fraction.
Provide your answer below: 7/
11. A spinner contains the numbers 1 through 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.
Provide your answer below: 34/
12. A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 4?
Provide your answer below: 38/
13. Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 0.718 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.)
p=0.282, n= p=0.718, n= p=0.718, n= p=0.282, n=
(The parameters p and n represent the probability of success on any given trial and the total number of trials,
respectively. In this case, success is winning a game, so p=0.718. The total number of trials, or games, is n=20)
14. A weighted coin has a 0.55 probability 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.)
18. Give the numerical value of the parameter p in the following binomial distribution scenario.
A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, wewant 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.
Provide your answer below: 0.
(The parameters p and n represent the probability of success on any given trial and the total number of trials,
respectively. In this case, success is a strike, so p=0.675)
19. Identify the parameters p and n in the following binomial distribution scenario.
Jack, a bowler, has a 0.38 probability of throwing a strike and a 0.62 probability of not throwing a strike. Jack bowls 20 times (Consider that throwing a strike is a success.)
Select the correct answer below:
p=0.38,n=0. p=0.38,n= p=0.38,n= p=0.62,n= p=0.62,n= (In a binomial distribution, there are only two possible outcomes. p denotes the probability of the event or trial
resulting in a success. In this scenario, it would be the probability of Jack bowling a strike, which is 0.38.
The total number of repeated and identical events or trials is denoted by n. In this scenario, Jack bowls a total of 20 times, so n=20).
20. The Stomping Elephants volleyball team plays 30 matches in a week-long tournament.
On average, they win 4 out of every 6 matches. What is the mean for the number of matches that they win in the tournament?
Select the correct answer below:
22. Identify the parameter n in the following binomial distribution scenario. A weighted coin has
a 0.441 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.)
Select the correct answer below:
23. Give the numerical value of the parameter n, the number of trials, in the following binomial distribution scenario.
A weighted coin has a 0.486 probability of landing on heads and a 0.514 probabilityof 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.
Provide your answer below: 27
24. The probability of winning on an arcade game is 0.659. If you play the arcade game 30 times, what is the probability of winning exactly 21 times?
- Round your answer to two decimal places.
Provide your answer below:.
25. The probability of buying a movie ticket with a popcorn coupon is 0.526. If you buy 26 movie tickets, what is the probability that exactly 15 of the tickets have popcorn coupons?
- Round your answer to three decimal places.
Provide your answer below:.
26. The probability of buying a movie ticket with a popcorn coupon is 0.608. If you
Participants
stopped
smoking
did not stop
smoking
Tota
l
given e-cigarette 11 21 32
not given e-
cigarette
Total 11 37 48
Provide your answer below:.
27. A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them arestrikes? (Round your answer to 3 decimal places if necessary.)
Provide your answer below:.
28. 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 given 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 chosen participant did not stop smoking, given that the participant received an e-cigarette?
Select the correct answer below:
29. Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the relative risk of flying for those birds that have long beaks? Round your answer to two decimal places.
- Marginal distributions are the row and column percentages. Breakfast and lunch are in the rows, so use the row totals to determine the percentages. The "Breakfast" percentage is 311/994≈0.31, and the "Lunch" percentage is 683/994≈0.69. The marginal distribution is 31%, 69%. 31. 155 fitness center members were asked if they run and if they lift weights. The results are shown in the table below.
Does not Run Runs Total Does not Lift Weights (^) 30 68 98 Lifts Weights (^) 16 41 57 Total (^) 46 109 155
Given that a randomly selected survey participant does not run, what is the probability that the
participant lifts weights?
- Enter the answer as a fraction.
Provide your answer below: 16/46 = 8/
32. Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
Provide your answer below: 35
33. Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown 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.
Students Have a dog Do^ not^ have^ a
dog
Total
Have a cat 35 25 60
Do not have a cat 27 11 38
Total 62 36 98
Not a long beak 7 13 20
Total 18 16 34
Provide your answer below: 6.
(The odds that a bird that flies also has long beak are 11 to 7. The odds that a bird that does not fly also has
long beak are 3 to 13. The odds ratio is then 11/17 / 3/13≈6.81. In this study, birds that fly had almost 7 times the odds of also having long beaks as the birds that do not fly.)
34. Fill in the following contingency table and find the number of students who both watch comedies AND watch dramas.
Students Watch dramas Do^ not^ watch dramas
Total
Watch comedies 16 25 41
Do not watch
comedies
Total 54 52 106
Provide your answer below: 16
35. Researchers wanted to study if couples having children are married. They surveyed a large groupof people. The data are shown 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.
Children No Children Total
Married 97 35 132
Not Married 68 71 139
Total 165 106 271
The odds that a married couple has children are 97 to 35. The odds that an unmarried couple has children
are 68 to 71. The odds ratio is then 97/35 ÷ 68/71 ≈ 2.89. In this study, people who are married had
about 3 times the odds of having children as people who are not married.
36. 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
