imc

In order to obtain an odd sum, exactly one out of the two dice must have an odd number. We can easily find the total probability using casework. Case 1: The first die is odd and the second die is even. The probability of this happening is $\frac{4}{6}\times \frac{4}{6}=\frac{16}{36}=\frac{4}{9}$ Case 2: The first die is even and the second die is odd. The probability of this happening is $\frac{2}{6}\times \frac{2}{6}=\frac{4}{36}=\frac{1}{9}$ Adding these two probabilities will give us our final answer. $\frac{4}{9}+\frac{1}{9}=\boxed{\frac{5}{9}}$ If you run out of time, you can see it is obviously greater than $\frac{1}{2}$ so it narrows guesses.