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A contract pays, in dollars, the number shown on one roll of a fair $6$ -sided die. You are told the roll is even. What is the contract's new fair value in dollars?

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Hint

Only the even faces remain possible, all equally likely.

Solution

The remaining faces are $2$ , $4$ and $6$ , each equally likely.
Their average is $(2 + 4 + 6) \div 3$ .
The new fair value is $4$ .

Answer: $4$

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