1. **State the problem:** We want to find the probability that at least one of the two customers buys a vanilla ice cream. 2. **Understand the tree diagram:** The first customer can buy vanilla with probability $\frac{2}{7}$ or strawberry with probability $\frac{5}{7}$. The second customer also has the same probabilities depending on the first customer's choice. 3. **Calculate the probability that neither customer buys vanilla:** This means both buy strawberry. $$P(\text{both strawberry}) = \frac{5}{7} \times \frac{5}{7} = \frac{25}{49}$$ 4. **Use the complement rule:** The probability that at least one buys vanilla is $$P(\text{at least one vanilla}) = 1 - P(\text{both strawberry}) = 1 - \frac{25}{49} = \frac{24}{49}$$ 5. **Final answer:** $$\boxed{\frac{24}{49}}$$ This means there is a $\frac{24}{49}$ chance that at least one customer buys vanilla ice cream.