Two dice are rolled. Find the probability that the sum of the numbers obtained is 5 given the sum is odd.

To solve the problem, we need to determine the probability that the sum of the numbers rolled on two dice is 5, given that the sum is odd.

### Step 1: Total outcomes where the sum is odd
For two dice, the sum is odd when one die shows an odd number and the other shows an even number.

- The odd numbers on a die are: 1, 3, 5.
- The even numbers on a die are: 2, 4, 6.

For each combination, we can either have:
- The first die odd and the second die even.
- The first die even and the second die odd.

Each die has 3 possibilities for odd and 3 possibilities for even, leading to:
- \(3 \times 3 = 9\) outcomes where the sum is odd for each of the two cases (odd-even or even-odd).

Thus, the total number of outcomes where the sum is odd is:
\[
9 + 9 = 18


Explore how to solve the conditional probability problem of finding the chance of rolling a sum of 5 with two dice given the sum is odd. This detailed step-by-step guide covers essential probability concepts, including the conditional probability formula and combinatorial analysis. Suitable for students in Grades 9-12.

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