There are 9 odd sums that you can get from rolling two dice.
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The two dice can be (odd, odd), (odd, even), (even, odd), or (even, even). Thus the probability of two dice totaling an even number is 2*(1/2)*(1/2) = 1/2. 50/50
The probability for a normal die is 1/2.
Three out of six which reduces to one half.