1. **Stating the problem:** A number is selected from the set $\{1, 2, 3, \ldots, 48, 49, 80\}$. Given that the number is divisible by 7, we want to find the probability that it is odd. 2. **Understanding the problem:** We are dealing with conditional probability. The formula for conditional probability is: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where: - $A$ is the event "number is odd" - $B$ is the event "number is divisible by 7" 3. **Identify the numbers divisible by 7 in the set:** The set is $\{1, 2, 3, \ldots, 49, 80\}$. Numbers divisible by 7 between 1 and 80 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 4. **Count the total numbers divisible by 7:** There are 11 numbers divisible by 7. 5. **Identify which of these are odd:** Odd multiples of 7 are 7, 21, 35, 49, 63, 77. There are 6 odd numbers divisible by 7. 6. **Calculate the probability:** $$P(\text{odd} | \text{divisible by 7}) = \frac{\text{number of odd divisible by 7}}{\text{total divisible by 7}} = \frac{6}{11}$$ **Final answer:** $$\boxed{\frac{6}{11}}$$