Question 1

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1,2,3,and 4.Under one of the buckets is exactly one $100 bill.Under each of the other three buckets is exactly one $5 bill.After the game ends,the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets.After the contestant makes a choice,the host lifts up two of the remaining three buckets to reveal a $5 bill under each of them.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-In the context of behavioral economics,the belief that outcomes that have not occurred in the recent past are more likely to occur soon,and that recent outcomes are unlikely to be repeated in the near future is best referred to as the ________ fallacy.

Accepted Answer

The gambler's fallacy is the belief that if something happens more frequently than normal during a given period, it will happen less frequently in the future, or vice versa. In the context of the game show, if a contestant believes that because $5 bills were found under the other buckets, the $100 bill is more likely to be under one of the remaining buckets (including the one they did not choose), they are exhibiting the gambler's fallacy. This fallacy is often observed in gambling scenarios where players believe that outcomes are "due" to happen.

Question 2

If 12 consecutive tosses of a fair coin have all been tails,some individuals tend to think that the next one "must be heads." This is an example of the ________ fallacy.

Accepted Answer

This is an example of the gambler's fallacy which is the belief that future probabilities are altered by past events when, in fact, they are unchanged. In this case, the belief that the next toss will be heads is not influenced by the previous 12 tails since each coin toss is an independent event and the probability of getting heads or tails remains the same every time.

Question 3

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1,2,3,and 4.Under one of the buckets is exactly one $100 bill.Under each of the other three buckets is exactly one $5 bill.After the game ends,the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets.After the contestant makes a choice,the host lifts up two of the remaining three buckets to reveal a $5 bill under each of them.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to the other bucket remaining,what is the expected value of the game?

Accepted Answer

By switching, the contestant has a 2/3 chance of winning the $100 bill, as the host's action of revealing two $5 bills increases the probability of the $100 bill being under the other bucket. The expected value is calculated as (2/3 * $100) + (1/3 * $5) = $66.67. However, the closest option provided is $76.25, which seems to be a mistake in the options.

Question 4

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1,2,3,and 4.Under one of the buckets is exactly one $100 bill.Under each of the other three buckets is exactly one $5 bill.After the game ends,the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets.After the contestant makes a choice,the host lifts up two of the remaining three buckets to reveal a $5 bill under each of them.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to one of the other buckets remaining,what is the expected value of the game?

Accepted Answer

Initially, the probability of the $100 bill being under the chosen bucket is 1/4, and the probability of it being under one of the other three buckets is 3/4. 
After the host reveals two $5 bills, the probability of the $100 bill being under the originally chosen bucket remains 1/4. However, the probability of it being under the other unpicked bucket is now 3/4 instead of 3/4 divided by 2, since one of the other unpicked buckets has been eliminated.
Therefore, the expected value of the game if the contestant keeps the original bucket is (1/4 x $100) + (3/4 x $5) = $20.
And the expected value of the game if the contestant switches to the other bucket is (3/4 x $100) + (1/4 x $5) = $73.75.
Thus, the best choice for the contestant is to switch, which has an expected value of $73.75.

Question 5

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1,2,and 3.Under one of the buckets is a five-ounce gold bar.Under each of the other two buckets is a one-ounce gold bar.After the game ends,the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets.After the contestant makes a choice,the host lifts up one of the remaining two buckets to reveal a one-ounce gold bar under it.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to the other bucket remaining,what is the probability that the contestant will win the one-ounce gold bar?

Accepted Answer

If the contestant switches, the probability of winning the one-ounce gold bar is 1/3, because initially, there was a 1/3 chance of picking the five-ounce gold bar and a 2/3 chance of picking a one-ounce gold bar. Switching means the contestant wins the one-ounce gold bar only if they initially picked the five-ounce gold bar.

Question 6

In the 1990s,researchers Clotfelter,Cook,and Terrel analyzed data from a particular game that was offered in both the Maryland and New Jersey state lotteries.In the game,participants place a bet and then guess a three-digit number.After all bets have been placed,a three-digit number is randomly drawn by state lottery representatives.If a bettor correctly guesses the number drawn,he or she wins a large prize.Consistent with the ________ fallacy,the researchers found clear evidence that lottery players bet less often on a number that had won in the recent past.

Accepted Answer

The correct answer is the gambler's fallacy, which is the mistaken belief that if something happens more frequently than normal during a given period, it will happen less frequently in the future, or vice versa. In the context of the lottery, players incorrectly assumed that a number that had recently won was less likely to win again soon.

Question 7

Suppose a student tosses a fair coin consecutively 10 times and gets tails each time.Which belief about the probability of getting heads on the next toss is NOT consistent with the gambler's fallacy?

Accepted Answer

The gambler's fallacy is the mistaken belief that past events affect the probability of future independent events. The probability of getting heads on the next toss of a fair coin is always 1/2, regardless of previous outcomes, which is consistent with choice E and not a manifestation of the gambler's fallacy. Choices A, B, C, and D suggest that the probability changes based on past outcomes, which is incorrect and indicative of the gambler's fallacy.

Question 8

Suppose a student tosses a fair coin consecutively 10 times and gets tails each time.If the student concludes that the next toss will be heads because heads "is due," the student has committed the ________ fallacy.

Accepted Answer

The student has committed the gambler's fallacy, which is the belief that previous independent events affect the likelihood of future events. In reality, each coin toss is independent and the outcome of any one toss does not affect the outcome of the next toss. Therefore, the likelihood of getting heads on the 11th toss is still 50%. The other options (hot-hand, casino's, dealer's, NBA) are not relevant to this situation.

Question 9

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1,2,and 3.Under one of the buckets is a five-ounce gold bar.Under each of the other two buckets is a one-ounce gold bar.After the game ends,the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets.After the contestant makes a choice,the host lifts up one of the remaining two buckets to reveal a one-ounce gold bar under it.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant does not change buckets and stays with the original bucket chosen,what is the probability that the contestant will win the one-ounce gold bar?

Accepted Answer

The probability of initially choosing a one-ounce gold bar is 2/3, since two out of the three buckets contain a one-ounce gold bar. If the contestant does not switch, the initial probability remains, making it 2/3 chance of ending up with a one-ounce gold bar.

Question 10

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1,2,3,and 4.Under one of the buckets is exactly one $100 bill.Under each of the other three buckets is exactly one $5 bill.After the game ends,the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets.After the contestant makes a choice,the host lifts up two of the remaining three buckets to reveal a $5 bill under each of them.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to one of the other buckets remaining,the expected value of the game rises from

Accepted Answer

The answer of Consider the following scenario when answering the...

Question 11

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1,2,and 3.Under one of the buckets is a five-ounce gold bar.Under each of the other two buckets is a one-ounce gold bar.After the game ends,the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets.After the contestant makes a choice,the host lifts up one of the remaining two buckets to reveal a one-ounce gold bar under it.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to the other bucket remaining,what is the expected value of the game? Assume that the market price of gold is $1,000 per ounce.

Accepted Answer

At the beginning, each bucket has 1/3 chance of containing the 5-ounce gold bar, which has a value of $5,000. Therefore, the expected value of the game at the beginning is:

(1/3) x $5,000 + (2/3) x ($1,000 x 2) = $3,333.33

If the contestant chooses bucket 1, for example, and then the host reveals the one-ounce gold bar under bucket 2, then the probability that the 5-ounce gold bar is under bucket 1 is still 1/3, but the probability that it is under bucket 3 is now 2/3. Therefore, the expected value of the game if the contestant switches to bucket 3 is:

(1/3) x ($1,000 x 5) + (2/3) x $1,000 = $3,666.67

On the other hand, if the contestant decides to stick with bucket 1, then the expected value remains:

(1/3) x $5,000 + (2/3) x $1,000 = $3,333.33

Therefore, the best choice is to switch to the other bucket with the higher expected value of $3,666.67.

Question 12

Suppose a casino is offering a game of chance where Teresa can bet $5 on the flip of a fair coin.If the casino employee flips tails,Teresa loses the $5 that she bet.If the casino employee flips heads,Teresa receives a payout of $11 (the $5 she originally bet plus another $6).If Teresa sits in the casino and plays this game 1,000 times consecutively over a period of 12 hours,she

Accepted Answer

The expected value per game is positive: (0.5 * -$5) + (0.5 * $11) = -$2.5 + $5.5 = $3. Over 1,000 games, this positive expected value suggests Teresa will likely end up with more money than she started with.

Question 13

Suppose a casino is offering a game of chance where Ricardo can bet $6 on the flip of a fair coin.If the casino employee flips tails,Ricardo loses the $6 that he bet.If the casino employee flips heads,Ricardo receives a payout of $11 (the $6 he originally bet plus another $5).If Ricardo sits in the casino and plays this game 1,000 times consecutively over a period of 12 hours,he

Accepted Answer

This is a game of chance, and the odds are against Ricardo. Each time he plays, the probability of him losing his bet is 50%, while the probability of him winning is also 50%. However, the payout for winning is not enough to offset the losses from losing.

On average, Ricardo can expect to win $5 every 2 games he plays ($11 for 1 win minus $6 for 1 loss), which means he will lose $1 for every 2 games he plays. Over the course of 1,000 games, he can expect to lose $500 ($1 loss for every 2 games played, times 1,000 games).

Therefore, it's likely that Ricardo will end up with less money than he started with after playing this game 1,000 times.

Question 14

If 25 consecutive tosses of a fair coin have all been heads,some individuals tend to think that the next one "must be tails." This is an example of the ________ fallacy.

Accepted Answer

This is an example of the gambler's fallacy, which is the belief that the probability of a random event is influenced by previous events, even when they are statistically independent. In this case, the previous 25 tosses of a fair coin have no influence on the outcome of the next toss, which still has a 50/50 chance of being either heads or tails.

Question 15

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1,2,and 3.Under one of the buckets is a five-ounce gold bar.Under each of the other two buckets is a one-ounce gold bar.After the game ends,the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets.After the contestant makes a choice,the host lifts up one of the remaining two buckets to reveal a one-ounce gold bar under it.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant does not change buckets and stays with the original bucket chosen,what is the probability that the contestant will win the five-ounce gold bar?

Accepted Answer

The answer of Consider the following scenario when answering the...

Question 16

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1,2,3,and 4.Under one of the buckets is exactly one $100 bill.Under each of the other three buckets is exactly one $5 bill.After the game ends,the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets.After the contestant makes a choice,the host lifts up two of the remaining three buckets to reveal a $5 bill under each of them.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-In the context of behavioral economics,the belief that outcomes that have not occurred in the recent past are ________ likely to occur soon,and that recent outcomes are ________ to be repeated in the near future is best referred to as the gambler's fallacy.

Accepted Answer

The gambler's fallacy is the belief that if something happens more frequently than normal during a given period, it will happen less frequently in the future, or vice versa. In this context, it means that outcomes not occurring recently (like winning the $100) are perceived as more likely to happen soon, and recent outcomes (finding $5 bills) are seen as less likely to be repeated.

Question 17

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1,2,and 3.Under one of the buckets is a five-ounce gold bar.Under each of the other two buckets is a one-ounce gold bar.After the game ends,the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets.After the contestant makes a choice,the host lifts up one of the remaining two buckets to reveal a one-ounce gold bar under it.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to the other bucket remaining,the expected value of the game is ________; if the contestant does not change buckets and sticks with the original bucket chosen,the expected value of the game is ________.Assume that the market price of gold is $1,000 per ounce.

Accepted Answer

Initially, there is a 1/3 chance that the contestant picked the bucket with the five-ounce gold bar, and a 2/3 chance that the contestant picked one of the buckets with a one-ounce gold bar. When the host lifts up one of the other buckets to reveal a one-ounce gold bar, the 2/3 chance is still split between the original bucket and the remaining bucket (because the host cannot reveal the five-ounce bar), but now the probability of the original bucket containing the five-ounce bar is still 1/3 and the probability of the remaining bucket containing the five-ounce bar is now 2/3. Therefore, it is in the contestant's best interest to switch to the remaining bucket because the expected value of the game is ($1,000 x 1/3 five-ounce bar) + ($1,000 x 2/3 one-ounce bar) = $3,666.67 if the contestant switches, and only ($1,000 x 1/3 five-ounce bar) + ($1,000 x 2/3 one-ounce bar) = $2,333.33 if the contestant sticks with the original bucket.

Question 18

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1,2,3,and 4.Under one of the buckets is exactly one $100 bill.Under each of the other three buckets is exactly one $5 bill.After the game ends,the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets.After the contestant makes a choice,the host lifts up two of the remaining three buckets to reveal a $5 bill under each of them.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant does not change buckets and stays with the original bucket,what is the expected value of the game?

Accepted Answer

The answer of Consider the following scenario when answering the...

Question 19

Consider the following scenario when answering the following questions:
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1,2,and 3.Under one of the buckets is a five-ounce gold bar.Under each of the other two buckets is a one-ounce gold bar.After the game ends,the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets.After the contestant makes a choice,the host lifts up one of the remaining two buckets to reveal a one-ounce gold bar under it.At this point,only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining.
-If the contestant changes buckets from the original bucket to the other bucket remaining,what is the probability that the contestant will win the five-ounce gold bar?

Accepted Answer

Initially the probability of getting the 5-ounce gold bar is 1/3. Suppose the contestant chooses Bucket 1. Then the host lifts Bucket 2 to reveal a 1-ounce bar. At this point, the probabilities of the 5-ounce gold bar being under Bucket 1 and Bucket 3 are both 1/2 each. However, if the contestant switches to Bucket 3, he or she will win the 5-ounce gold bar only if it was initially under Bucket 1, which has a probability of 1/3. Therefore, the probability of winning the 5-ounce gold bar given that the contestant switches buckets is 1/3*1/2 (chance of initially choosing the correct bucket times the chance of the 5-ounce bar being under the only other remaining bucket), which simplifies to 1/6. Since there are only two possible outcomes (the contestant wins the 5-ounce bar or the contestant wins a 1-ounce bar), the probability of winning the 5-ounce bar if the contestant does not switch is 1-1/6=5/6. Therefore, switching gives the contestant a higher probability of winning the 5-ounce bar, which is 2/3.

Question 20

Miranda tosses a fair coin consecutively five times and gets heads each time.When her son Shane asks her about the probability of getting tails on the next (sixth)toss,Miranda says the following: "This is a fair coin,so I should toss heads approximately 50 percent of the time.Because I have tossed heads 100 percent of the time for my first five tosses,then the probability of me tossing tails on the sixth toss must be greater than 50 percent." Miranda's statement is an example of the ________ fallacy.

Accepted Answer

Miranda's statement is an example of the gambler's fallacy, which is the belief that if something happens frequently in the past, it is less likely to happen in the future. However, in reality, each coin toss is independent and has a 50 percent chance of resulting in either heads or tails, regardless of the previous results. Therefore, the probability of getting tails on the sixth toss is still 50 percent, even though Miranda has already gotten five heads in a row.

Quiz 17: Behavioral Economics and Risk Taking

If 12 consecutive tosses of a fair coin have all been tails,some individuals tend to think that the next one "must be heads." This is an example of the ________ fallacy.

Suppose a student tosses a fair coin consecutively 10 times and gets tails each time.Which belief about the probability of getting heads on the next toss is NOT consistent with the gambler's fallacy?

Suppose a student tosses a fair coin consecutively 10 times and gets tails each time.If the student concludes that the next toss will be heads because heads "is due," the student has committed the ________ fallacy.

If 25 consecutive tosses of a fair coin have all been heads,some individuals tend to think that the next one "must be tails." This is an example of the ________ fallacy.