Consider the following scenario when answering the next two questions:Imagine a television same show where one lucky contestant is presented with four upside-down buckets numbered 1,2,3, and 4 . Under one of the buckets is $10,000. Under each of the other three buckets is $20. 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 up two of the remaining three buckets to reveal $20 under each of them. At this point, only two buckets remain uncovered: the bucket 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 remaining bucket.
If the contestant changes buckets from the original bucket to the other remaining bucket, what is the expected value of the game?
$4,650
$3,760
$7,505
$2515
$1.725
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