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Week 4 Homework Questions Probability
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 (Mutually exclusive events are events that cannot occur together. In this case, drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards are two events that cannot possibly occur together.)
5. 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 picked at
random, what is the probability that the card has an ODD number? Select the correct answer below: 10/ 8/ 14/ 6/
(By counting, we can see that there are 8 odd cards, and a total of 15 cards in the deck. So the probability is 8/15).
6. Hector is a baseball fan but wants to watch something different. There are 5 basketball games, 2 football games, and 4 hockey games that he can choose to watch. If Hector randomly chooses a game, what is the probability that it is a basketball game? Give your answer as a fraction. Provide your answer below: 5/
7. There are 26 cards in a hat, each of them containing a different letter of the alphabet. If one
card is chosen at random, what is the probability that it is not between the letters L and P, inclusive? Provide your answer below: 21/
8. A spinner contains the numbers 1 through 80. What is the probability that the spinner will
land on a number that is not a multiple of 12?
Give your answer in fraction form. Provide your answer below: 74/
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.) Provide your answer below: 0.
(This probability can be found using the binomial distribution with success probability p=0.55 and 14 trials. To find
the probability that exactly 9 of the tosses are heads, use a calculator or
computer: P(X= 9 )=binompdf( 14 ,0.55, 9 )≈0.170.
15. Identify the parameter p in the following binomial distribution scenario. The probability of buying
a movie ticket with a popcorn coupon is 0.546 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.) Select the correct answer below:
16. A softball pitcher has a 0.64 probability 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? Round your answer to three decimal places. 0.
This probability can be found using the binomial distribution with success probability p=0.64 and 20 trials. To find
the probability that exactly 13 of the pitches are strikes, use a calculator or
computer: P(X= 13 )=binompdf( 20 ,0.64, 13 )=0.184.
17. Identify the parameter n in the following binomial distribution scenario. A basketball
player has a 0.429 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.) Select the correct answer below:
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, 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. 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).
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: 5 14 19 24
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 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. 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
buy 10 movie tickets, what is the probability that more than 3 of the tickets have
popcorn coupons? (Round your answer to 3 decimal places if necessary.)
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 are
strikes? (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?
Participants
stopped
smoking
did not stop
smoking
Tota
l
given e-cigarette 11 21 32
not given e-
cigarette
Total 11 37 48
Select the correct answer below: 21/ 11/ 11/
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.
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
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.
Flies Does not fly Total
Long beak 11 3
Not a long beak 7 13 20
Total 18 16
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
Do not watch
comedies
Total 54 52
Provide your answer below: 16
35. Researchers wanted to study if couples having children are married. They surveyed a large group of 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
5.51; The advertisement was successful. 2.35; The advertisement was successful. 1.79; The advertisement was successful. 0.56; The advertisement was not successful. 0.43; The advertisement was not successful. 0.18; The advertisement was not successful.
( The odds that a student targeted by the advertisement registers to vote is 103 to 36. The odds that a student not
targeted by the advertisement registers to vote is 78 to 64 , or 39 to 32. The odds ratio is then 103/36 ÷
39/32≈2.35. In this situation, students targeted by the advertisement had more than twice the odds of registering to
vote as students not targeted by the advertisement. It would appear that the advertisement was successful)
38. Researchers wanted to study if wearing cotton clothes is related to depression. They surveyed a large group of people. The data are shown in the contingency table below. What is the relative risk of wearing cotton clothes for those who are depressed? Round your answer to two decimal places. Depressed Not Depressed Total Cotton 122 189 311 Not Cotton 420 263 683 Total 542 452 994 Answer:. ( The probability that someone who is depressed wears cotton clothes is 122542. The probability that someone who is
not depressed wears cotton clothes is 189452. The relative risk is then 122542189452 ≈0.54. This means that in this
survey, depressed people were 54 % as likely to wear cotton clothes as people who are not depressed)
39. 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 shown 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.
Afraid of
heights
Not afraid of
heights
Tota
l
Afraid of flying 76 33 109
Not afraid of
flying
Total 158 404 561
Provide your answer below: 5.
(The probability that someone with a fear of heights is afraid of flying is 76/158=38/79. The probability that
someone who does not have a fear of heights is afraid of flying is 33/403. The relative risk is then 38/79 /v
33/403≈5.87. This means that in this survey, people with a fear of heights were 587 % as likely to have a
fear of flying as people without a fear of heights.
40. A study of drivers with speeding violations in the last year and drivers who use cell phones produced the following fictional data:
Violatio
n
No
violation
Tota
l
Cell phone user 25 280 305
Not a cell phone
user
Total 70 685 755
Find the probability that a driver received a violation, given that the driver is a cell phone user. Select the correct answer below: 280/ 70/ 25/ 25/
41. Find the probability that a randomly chosen person takes public transit to work given that the person does not support the environmental bill.
odds ratio for people having children to be married against people not having children to be married? Round your answer to two decimal places. Children No Children Total Married 97 35 132 Not Married 68 71 139 Total 165 106 271 Provide your answer below: 2.
(The odds that people having children are married are 97 to 68. The odds that people not having children
are married are 35 to 71. The odds ratio is then 97/68 ÷ 35/71≈2.89. In this study, people who have children
had about 3 times the odds of being married as people who do not have children)
45. Researchers wanted to study if wearing cotton clothes is related to depression. They surveyed a large group of people. The data are shown in the contingency table below. What is the odds ratio for people wearing cotton clothes being depressed against people not wearing cotton clothes being depressed? Round your answer to two decimal places. Depressed Not Depressed Total Cotton 122 189 311 Not Cotton 420 263 683 Total 542 452 994 Provide your answer below: 0.
(The odds that a person who wears cotton clothes is also depressed are 122 to 189. The odds that a
person who does not wear cotton clothes is depressed are 420 to 263. The odds ratio is then 122/189 ÷
420/263≈0.40. In this study, people who wear cotton clothes had over 0.4 times the odds of also being
depressed as people who are not wearing cotton clothes.
46. Review the flu vaccine data below. What is the odds ratio of not catching the flu for those who receive the new vaccine?
Caught
flu
Did not catch
flu
Tota
l
New Vaccine 15 375 390
Traditional
Vaccine
Total 70 600 670
Answer: 6.
The odds that a person who receives the new vaccine does not catch the flu is 375 to 15 , or 25 to 1.
The odds that a person who receives the traditional vaccine does not catch the flu is 225 to 55 ,
or 45 to 11. The odds ratio is then 25/1 ÷ 45/11≈6.11. In this experiment, people who took the new vaccine
had just over 6 times the odds of not catching the flu as people who did not take the new vaccine.
47. 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 shown in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.
Insomni
a
No
insomnia
Tota
l
New drug 52 226 278
Traditional
drug
Total 88 521 609
Answer: 1.
(The probability that a patient who receives the new drug develops insomnia is 52/278=26/139.
The probability that a patient who receives the traditional drug develops insomnia is 36/331. The relative risk
is then 26/139 ÷ 36/331≈1.72. This means that in this study, people who took the new drug were 172 % more
likely to develop insomnia.
50. Kelsey, a basketball player, hits 3 -point shots on 38.1% 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. Round your answer to three decimal places. Provide your answer below: 0.
51. A computer graphics card manufacturer is testing an improvement to its production
process. If a sample of 100 graphics 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 0.9%, will the manufacturer switch to the new production process?
Select the correct answer below: Yes, because the probability of having 3 or more defective graphics cards is greater than 0.10. Yes, because the probability of having 3 or more defective graphics cards is less than 0.10. No, because the probability of having 3 or more defective graphics cards is less than 0.10. No, because the probability of having 3 or more defective graphics cards is greater than 0.10.
(Note that this is a cumulative binomial probability. In this case, we want to find the probability of 3 or more
successes, inclusive, where a success is one of the graphics cards being defective. The probability of
having 2 or fewer defective graphics cards is the complement of the probability of having 3 or more defective
graphics cards. To determine the probability from a binomial distribution using Excel, follow the steps below.
- First press FORMULAS and then INSERT FUNCTION.
- Then select the BINOM.DIST function.
- Next enter the values for the number of successes, the number of trials, the probability of a success, and
the number of successes. In this case, enter 2 , 100 , and 0.009, in that order.
Enter 1 for Cumulative since this is a cumulative probability.
4. Press OK. Excel should then display the probability. Here, the resulting probability is 0.937964, which
is 0.938 rounded to three decimal places.
To find the probability of having 3 or more defective graphics cards, subtract this probability from 1. The
probability of having 3 or more defective graphics cards is 1−0.938=0.062, which is less than 0.10.
So, the manufacturer will switch to the new process)
52. In a large city’s recent mayoral election, 126,519 out of 283,143 registered voters
actually turned out to vote. If 20 registered voters are randomly selected, find the
probability that exactly 8 of them voted in the mayoral election. Use Excel to find the
probability. Round your answer to three decimal places. Provide your answer below: 0. P=.446 (126,519/283,143) N=20 X=
53. Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a
polygraph test on a random sample of 12 individuals. 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. Select the correct answer below: Alex will conclude that the test is reliable since the probability of no false positives is less than 0.5. Alex will conclude that the test is not reliable since the probability of no false positives is greater than 0.5. Alex will conclude that the test is not reliable since the probability of no false positives is less than 0.5. Alex will conclude that the test is reliable since the probability of no false positives is greater than 0.5. ( Next enter the values for the number of successes, the number of trials, the probability of a success, and the
number of successes. In this case, enter 0 , 12 , and 0.055, in that order. Enter 0 for Cumulative since
this is not a cumulative probability)
54. A certain cold remedy has an 88% rate of success of reducing symptoms
within 24 hours. 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.
Round your answer to three decimal places. 0.
55. Kevin works for a company that manufactures solar panels. In a large batch of solar
panels, about 1 in 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. Round your answer to three decimal places. 0.
