A pair of dice is rolled. find the probability of each

P (Odd sum)

P (Odd sum) = 1/2 or 50%

For two dice rolls to have an odd sum either the 1st one is even and the 2nd is odd or the 1st one is odd and the 2nd is even.

The chance for the 1st one being even is 1/2, same for 2nd being odd. So the chance that the 1st is even and the 2nd is odd is 1/2 * 1/2 = 1/4. This also applies for the 1st one being odd and the 2nd being even, so the chance that the 1st is odd and the 2nd is even is also 1/4.

So then you add these two probabilities, 1/4 + 1/4 = 1/2 which is the answer.