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"?

Accepted Answer

Out of the five friends, there are two whose names start with the letter "M" (Malik and Monique). Therefore, the probability of choosing a friend whose name starts with the letter "M" is 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

Accepted Answer

The statement means that in a very large number of Bridge deals, the percentage of deals on which each player has one ace will be close to 11%. Option A is incorrect as it only talks about 100 deals. Option B is incorrect as it talks about a specific range of deals and not the overall percentage. Option D is incorrect as it talks about the average number of aces per hand, which is not specified in the statement.

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?

Accepted Answer

Since the coin is fair, the probability of getting heads or tails is 1/2 each. Thus, the fraction of tosses resulting in heads is expected to be close to 1/2.

Option A is incorrect because the probability of getting more than 5000 heads is also 1/2. Option B is incorrect because the outcome of any coin toss is independent of the previous tosses. Option D is also incorrect because the outcomes of the tosses are independent, and hence the result of the 100th toss is not influenced by the previous tosses.

Question 4

If I toss a fair coin 5000 times

Accepted Answer

The answer of If I toss a fair coin 5000...

Question 5

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

Accepted Answer

The probability of getting a one on both dice is 1/36, which means that in the long run, the outcome of both dice being one will occur on 1/36 of all rolls. Option A is incorrect because it implies that only one roll out of 36 will have both dice be one, which is not the case. Option B is incorrect because it is the odds against the event happening, not the probability of it happening. Option C is incorrect because it is the average number of ones per roll, which is not equivalent to the probability of both dice being one.

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?

Accepted Answer

The answer of Suppose you have five friends: Malik, Samson,...

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?

Accepted Answer

Since you put the sandwich back into the bag, the probability of pulling out any specific sandwich is always 1/10, regardless of what you pulled out before. Therefore, the probability of pulling out the ham on rye again is 1/10.

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?

Accepted Answer

After removing the ham on rye sandwich, there are 9 sandwiches left in the bag: one BLT and eight bologna sandwiches. The probability of pulling out a bologna sandwich next is the number of bologna sandwiches divided by the total number of sandwiches left, which is 8/9.

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?

Accepted Answer

Since you put the ham on rye back into the bag, there are still 10 sandwiches in the bag and only 1 is a BLT. Therefore, the probability of pulling out the BLT next is 1/10.

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

Accepted Answer

The probability of being dealt a flush is the number of flush hands divided by the number of possible hands, which is: 
$$\frac{5148}{2598960} \approx 0.00198$$
This can also be written as $1/505.9$ which is closest to option C, 1/500.

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"?

Accepted Answer

The answer of Suppose you have five friends: Malik, Samson,...

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?

Accepted Answer

After removing the ham on rye, 9 sandwiches remain: 1 BLT and 8 bologna. The probability of pulling out the BLT next is 1 out of the remaining 9 sandwiches, or 1/9.

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:

Accepted Answer

The last two digits of the phone labeled 341 are 41. The chance of choosing the pair of digits 41 from all possible pairs is 1/100. Therefore, the chance of selecting the phone labeled 341 is 1/100.

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?

Accepted Answer

As the number of tosses increases, the probability of getting between 40% and 60% heads increases because the Law of Large Numbers suggests that the proportion of heads will approach the true probability of 50% as the number of tosses increases. On the other hand, the probability of getting exactly 50% heads decreases because there are more possible outcomes as the number of tosses increases, and only one of those outcomes results in exactly 50% heads.

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?

Accepted Answer

If Amy says the probability that she has the winning ticket is 1, it means she is certain to win. This can only happen if she has purchased all 1000 tickets, making her the sole participant and guaranteed winner.

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?

Accepted Answer

Since the ham on rye sandwich has already been pulled out and not replaced, it is impossible to pull it out again.

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?

Accepted Answer

The answer of Suppose you have five friends: Malik, Samson,...

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?

Accepted Answer

The probability of winning the largest prize on any given drawing is independent of previous outcomes, remaining at 0.001.

Question 19

The probability of an outcome of a random phenomenon is

Accepted Answer

The definition of probability is the long-term proportion of times that an event will occur in repeated trials of a random phenomenon. Therefore, option B accurately defines probability. Option A is incorrect because an outcome cannot have a probability of 0 or 1 unless it is impossible or certain, respectively. Option C is incorrect because the mean and standard deviation are not necessarily related to probability. Option D is incorrect because expected value is a measure of central tendency, not probability. Option E is incorrect because confidence level is a term used in statistical inference, not probability.

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?

Accepted Answer

The probability of earning a passing grade is given as 82%, which is equivalent to 0.82 as a decimal. Therefore, the probability of a randomly selected student earning a passing grade is 0.82.

Quiz 17: Thinking About Chance

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"?

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

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?

If I toss a fair coin 5000 times

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

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?

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

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"?

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?

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?

The probability of an outcome of a random phenomenon is

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?