Imagine a television game show where one lucky contestant is presented with four upside down-buckets numbered 1,2,3 and 4. Under one of the buckets is 100,000$. Under each of the other three buckets is 1000$. After the game ends, the contestant will receive the amount of money 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 1000$ under it. At this point, three buckets remain uncovered: the bucket 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 remaining buckets.
If the constant buckets from the original to one of the other remaining buckets, what is the probability that the contestant will win the $100,000?
A: ⅛
B: ½
C: ⅞
D: ⅝
E: ⅜