You roll two fair six-sided dice. Given that their sum is even, what is the probability that both dice show the same number?
Express as a fraction
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The sum is even when both dice are even or both are odd, giving 9+9=18 outcomes. Among those 18, the pairs where both show the same number are (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) — all 6 have even sums. So the probability is 186=31.