Imagine a Game Show on Television Where One Lucky Contestant $\frac { 1 } { 8 }$

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 large pile of $100 bills. 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 chosen, what is the probability that the contestant will win exactly one $5 bill?

A) $\frac { 1 } { 8 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 3 } { 4 }$
E) $\frac { 5 } { 8 }$