Two standard six-sided dice are to be rolled. If the sum is an even number greater than 7, then what is the probability that both dice are even? Express your answer as a common fraction.

The possible outcomes for a total>7

are { (2,6), (6,2), (3,5), (3,6), (5,3), (5,6),(4,4), (4,5), (4,6),(5,4),(6,4),(5,5), (5,6), (6,5), (6,6)}

= 15 outcomes

6 of these have two even numbers

Hence (both even and total >7) = 6/15 =2/5

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