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 a $100 bill. Under each of the other three buckets is a $10 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 one of the remaining three buckets to reveal a $10 bill under it. At this point, three buckets remain uncovered: the bucket that the contestant originally chose and the two buckets that were 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 one of the two other buckets remaining.

-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, the bettor wins a large prize. Consistent with the ___________, the researchers found clear evidence that lottery players bet less often on a number that had won in the recent past.

Question

Quizplus · Accepted Answer

The researchers found clear evidence of bettors being less likely to choose a number that had won in the recent past, which is consistent with the gambler's fallacy. This fallacy is the belief that the odds of a certain event happening increase or decrease based on recent occurrences of the event, even though the probability is actually independent of past outcomes.

Answer: Bucket 1
 After the host reveals a $10 bill under one of the remaining three buckets, the odds of the $100 bill being under the contestant's original choice (Bucket 1) increase from 1/4 to 1/3. It is statistically advantageous for the contestant to stick with their original choice.

Answer: $30
 There is a 1/3 chance that the $100 bill is under the contestant's original choice (Bucket 1) and a 2/3 chance that the bill is under one of the other two remaining buckets. Therefore, the expected value of the contestant's choice is (1/3 x $100) + (2/3 x $10) = $30.

Imagine a Game Show on Television Where One Lucky Contestant