1. **Problem statement:** Given Angela picks two numbers, one from \{1,2,3\} and one from \{4,5,6\}, and their sum is odd, find the probability that one of the numbers is 3. 2. **Understanding the problem:** The total sum is odd. We want $P(\text{one number is }3 \mid \text{sum is odd})$. 3. **Step 1: Identify all possible sums and their parity.** From the table: - When first number is 1: sums with second number 4,5,6 are 5,6,7 - When first number is 2: sums are 6,7,8 - When first number is 3: sums are 7,8,9 4. **Step 2: List all pairs with odd sums.** Odd sums are 5,7,9. Pairs with sum 5: (1,4) Pairs with sum 7: (1,6), (2,5), (3,4) Pairs with sum 9: (3,6) So odd sum pairs are: (1,4), (1,6), (2,5), (3,4), (3,6) 5. **Step 3: Count total odd sum outcomes:** There are 5 such pairs. 6. **Step 4: Count odd sum outcomes where one number is 3:** Pairs with 3 and odd sum: (3,4), (3,6) → 2 pairs. 7. **Step 5: Calculate the conditional probability:** $$ P(\text{one number is }3 \mid \text{sum is odd}) = \frac{\text{number of odd sum pairs with 3}}{\text{total odd sum pairs}} = \frac{2}{5} $$ **Final answer:** $$\boxed{\frac{2}{5}}$$