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Highest plus lowest

Expected valueEasy

$2$ fair $6$ -sided dice are rolled. You are paid the highest result plus the lowest result, in dollars. What is the expected payout?

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Hint

Think about what the highest plus the lowest of $2$ numbers equals.

Solution

For $2$ numbers, the larger plus the smaller is always their sum.
So the payout equals the sum of the $2$ dice, and each die averages $\frac{7}{2}$ .
The expected payout is $\frac{7}{2} + \frac{7}{2} = 7$ .

Answer: $7$