Deck 17: Thinking About Chance

Question 1

Suppose you have five friends: Malik, Samson, Quint, Jennifer, and Monique.
You randomly choose one of them to attend a basketball game with you. What is the probability that you choose a friend whose name starts with the letter "M"?

A) 2
B) 1/2
C) 2/3
D) 2/5
E) 3/5

Answer 1

2/5

Question 2

You read in a book about the card game Bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. This means that

A) in every 100 bridge deals, each player has one ace exactly 11 times.
B) in one million bridge deals, the number of deals on which each player has one ace will scarcely be within ±100 of 110,000.
C) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%.
D) in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11.

Answer 2

in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%.

Question 3

Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true?

A) It is unlikely that Dr. Stats will get more than 5000 heads.
B) Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head.
C) The fraction of tosses resulting in heads should be close to 1/2.
D) The chance that the 100th toss will be a head depends somewhat on the results of the first 99 tosses.
E) All statements are true.

Answer 3

The fraction of tosses resulting in heads should be close to 1/2.

Question 4

If I toss a fair coin 5000 times

A) the number of heads will be close to 2500.
B) the proportion of heads will be close to 0.5.
C) the proportion of heads in these tosses is a parameter.
D) the proportion of heads will be close to 50.

Question 5

When two six-sided die are rolled, the probability of getting a one on both is 1/36. This means that

A) of every 36 rolls, exactly 1 will have both die be one.
B) the odds against both die being one are 36 to 1.
C) in the long run, the average number of ones is 1/36.
D) in the long run the outcome that both die are one will occur on 1/36 of all rolls.

Question 6

Suppose you have five friends: Malik, Samson, Quint, Jennifer, and Monique.
You randomly choose one of them to attend a basketball game with you. What is the probability that you choose Quint?

A) 0.5 (either he is chosen or he isn't).
B) 5
C) 0.2
D) 0
E) 1

Question 7

Suppose you have a bag of 10 sandwiches from the deli: one bacon, lettuce, and tomato (BLT;) one ham on rye; and eight bologna sandwiches. You pull out one sandwich and discover that you've pulled out the ham on rye.
If you put the sandwich back into the bag, what is the probability that you pull out the ham on rye the next time you pull out a sandwich?

A) 0.5 (either you pull it out or you don't)
B) 1/10
C) 1/9
D) 0
E) 1

Question 8

Suppose you have a bag of 10 sandwiches from the deli: one bacon, lettuce, and tomato (BLT) one ham on rye; and eight bologna sandwiches. You pull out one sandwich and discover that you've pulled out the ham on rye.
If you do not put the sandwich back into the bag, what is the probability that you pull out a bologna sandwich the next time you pull one out?

A) 1/10
B) 1/9
C) 8/10
D) 8/9
E) 0

Question 9

Suppose you have a bag of 10 sandwiches from the deli: one bacon, lettuce, and tomato (BLT) one ham on rye; and eight bologna sandwiches. You pull out one sandwich and discover that you've pulled out the ham on rye.
If you put the sandwich back into the bag, what is the probability that you pull out the BLT the next time you pull out a sandwich?

A) 0.5 (either you pull out the BLT or you don't)
B) 1/10
C) 1/9
D) 0
E) 1

Question 10

There are 2,598,960 possible 5-card hands that can be dealt from an ordinary 52-card deck. Of these, 5148 have all five cards of the same suit. (In poker such hands are called flushes.) The probability of being dealt such a hand (assuming randomness) is closest to

A) 1/4.
B) 1/100.
C) 1/500.
D) 1/1000.
E) 1/5148.

Question 11

Suppose you have five friends: Malik, Samson, Quint, Jennifer, and Monique.
You randomly choose four of them to attend a basketball game with you. What is the probability that you choose at least one friend whose name starts with the letter "M"?

A) 4
B) 1/4
C) 1/5
D) 4/5
E) 1

Question 12

Suppose you have a bag of 10 sandwiches from the deli: one bacon, lettuce, and tomato (BLT) one ham on rye; and eight bologna sandwiches. You pull out one sandwich and discover that you've pulled out the ham on rye.
If you do not put the sandwich back into the bag, what is the probability that you pull out the BLT the next time you pull out a sandwich?

A) 0.5 (either you pull out the BLT or you don't)
B) 1/10
C) 1/9
D) 0
E) 1

Question 13

A Home Depot store receives a shipment of 500 cordless screwdrivers of the same model. The 500 boxes are labeled 0, 1, 2, 3, ... , 499. The inventory specialist at the store wishes to test five of the screwdrivers. She uses the table of random digits to choose a single pair of digits at random from all the possible pairs 00, 01, ... , 99. It happens that she chooses the pair 69. She then inspects all the phones whose labels end in the chosen pair of digits. In this case, she will inspect the phones with labels 69, 169, 269, 369, and 469. The chance that the phone labeled 341 would be one of those chosen was:

A) 1 in 500 (or 1/500).
B) 5 in 100 (or 5/100).
C) 1 in 100 (or 1/100).
D) 1 in 5 (or 1/5).

Question 14

As the number of tosses of a fair coin goes up from 10, to 100, to 1000, and to 10,000, what happens to the probability of getting between 40% and 60% heads? What happens to the probability of getting exactly 50% heads?

A) Both of those probabilities increase.
B) Both of those probabilities decrease.
C) The first probability increases, but the second one decreases.
D) The first probability decreases, but the second one increases.
E) We don't know until we toss the coin.

Question 15

A sorority is selling 1000 raffle tickets to raise money for a charity. The prize is a $100 gift card to the campus bookstore. Amy says that the probability that she has the winning ticket is 1. Assuming that there is no cheating and that all 1000 tickets are sold, how many raffle tickets does Amy have?

A) She has 1000 tickets.
B) She has 100 tickets.
C) She has 1 ticket.
D) There is not enough information to answer the question.

Question 16

Suppose you have a bag of 10 sandwiches from the deli: one bacon, lettuce, and tomato (BLT) one ham on rye; and eight bologna sandwiches. You pull out one sandwich and discover that you've pulled out the ham on rye.
If you do not put the sandwich back into the bag, what is the probability that you pull out the ham on rye the next time you pull out a sandwich?

A) 0.5 (either you pull it out or you don't)
B) 1/10
C) 1/9
D) 0
E) 1

Question 17

Suppose you have five friends: Malik, Samson, Quint, Jennifer, and Monique.
You randomly choose four of them to attend a basketball game with you. What is the probability that Jennifer is not chosen to attend the game with you?

A) 4
B) 1/4
C) 1/5
D) 4/5
E) 1

Question 18

Your roommate plays a Pick Three lottery game, with probability one in one thousand (0.001) of winning the largest prize. He has played every opportunity (daily, morning and night) for the past year, using his area code, and has never won-730 losses in a row. What is the probability he wins the largest prize on the next drawing?

A) 0.001
B) less than 0.001
C) greater than 0.001
D) 0
E) 1

Question 19

The probability of an outcome of a random phenomenon is

A) either 0 or 1, depending on whether or not the phenomenon can actually occur.
B) the proportion of a very long series of repetitions on which the outcome occurs.
C) the mean plus or minus two standard deviations.
D) another name for its expected value.
E) the confidence level.

Question 20

It is known that about 82% of Dr. Street's introductory statistics students pass his course. What is the probability that a randomly selected student from Dr. Street's current introductory statistics course will earn a passing grade?

A) 1/82
B) 0.82
C) 82
D) 0.50
E) 0.18

Question 21

A _____________ of an outcome is a number between 0 and 1 that expresses an individual's judgment of how likely the outcome is.

A) personal probability
B) expected value
C) correlation
D) randomness
E) possibility

Question 22

Just before winning the Belmont Stakes and becoming the first horse in 37 years to win the Triple Crown, the odds against racehorse #5 (named American Pharoah) winning the race were 3 to 5 (3:5 odds against winning). What did the oddsmakers consider the probability that American Pharoah would win that year's Belmont Stakes?

A) 3/5
B) 5/3
C) 0.375
D) 0.625
E) 0.35

Question 23

About 34% of people are expected to be infected by the flu this season. What is the risk that a randomly selected person will be infected by the flu?

A) 34
B) 0.34
C) 0.66
D) 66
E) 1 divided by the population size

Question 24

Suppose you studied very hard for this test, and you believe that the probability that you'll pass the test is 0.99. Which of the following statements is true?

A) The value 0.99 is a personal probability.
B) The value 0.99 indicates that you don't expect to pass the test.
C) You'll be surprised if you don't pass the test.
D) The value 0.99 is a personal probability, and the value 0.99 indicates that you don't expect to pass the test.
E) The value 0.99 is a personal probability, and you'll be surprised if you don't pass the test.

Question 25

The Virginia State Lottery Commission states that the probability of winning a prize in their new scratch-off ticket lottery is 0.31. What are the odds against winning a prize in this new lottery game?

A) 69
B) 69 to 31
C) 31 to 69
D) 31
E) 1 - 0.31 = 0.69