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?
A) $32.50
B) $40.00
C) $43.75
D) $66.25
E) $100.00

Question

Quizplus · 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.

Consider the Following Scenario When Answering the Following Questions