Consider the following scenario to answer the questions that follow.
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.
-If the contestant changes buckets from the original bucket to one of the other buckets remaining,what is the probability that the contestant will win the $100 bill?

Question

Quizplus · Accepted Answer

When the contestant initially chooses one bucket, there is a 1/4 chance that the $100 bill is under that bucket and a 3/4 chance that a $10 bill is under it. After the host reveals a $10 bill under one of the remaining buckets, there is still a 1/4 chance that the $100 bill is under the contestant's original choice and a 3/4 chance that it is under one of the other two remaining buckets. Since one of those two buckets definitely has a $10 bill and the other bucket may have a $100 bill or a $10 bill, the probability of winning the $100 bill if the contestant switches to the other bucket is 2/3 (since there are two equally likely possibilities for the remaining buckets: one with a $100 bill and one with a $10 bill). Thus, it is in the contestant's best interest to switch to the other bucket.

Consider the Following Scenario to Answer the Questions That Follow