Imagine a Game Show on Television Where One Lucky Contestant

question 7

Multiple Choice

Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1, 2, and 3. Under one of the buckets is a 5-oz. gold bar. Under each of the other two buckets is a 1-oz. gold bar. After the game ends, the contestant receives the gold bar that is under his or her bucket.
The host of the game show asks the contestant to choose one of the three buckets. After the contestant makes a choice, the host lifts up one of the remaining two buckets to reveal a 1-oz. gold bar under it. 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 the other bucket remaining, the expected value of the game is __________; if the contestant does not change buckets and sticks with the original bucket chosen, the expected value of the game is ___________. Assume that the market price of gold is $1,000.00 per ounce.

• A) $4,000.00; $4,000.00
• B) $2,333.33; $3666.67
• C) $3,666.67; $2333.33
• D) $5,000.00; $1,000.00
• E) $1,000.00; $5,000.00

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Definitions:

Currency

A system of money in general use in a particular country or economic context, also refers to the digital or physical form of money.

Auto

Short for "automatic," this term refers to functions or features that operate without manual intervention.

Integer

A whole number that can be positive, negative, or zero, not including fractions or decimals.

Currency Format

A way of displaying numbers in a specific monetary style, which includes symbols, decimal places, and digit grouping according to different cultural norms.