1. **State the problem:** A number is selected from the set $\{1, 2, 3, \ldots, 50\}$. Given that the number is divisible by 7, find the probability that it is odd. 2. **Identify the set of numbers divisible by 7 between 1 and 50:** These are $7, 14, 21, 28, 35, 42, 49$. 3. **Count the total numbers divisible by 7:** There are 7 such numbers. 4. **Identify which of these are odd:** The odd numbers divisible by 7 in this set are $7, 21, 35, 49$. 5. **Count the odd numbers divisible by 7:** There are 4 odd numbers. 6. **Use the probability formula:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ 7. **Calculate the probability:** $$\text{Probability} = \frac{4}{7}$$ **Final answer:** The probability that the number is odd given it is divisible by 7 is $\boxed{\frac{4}{7}}$.