1. **State the problem:** We want to find the probability that Xavier and Yvonne solve the problem, but Zelda does not. 2. **Given probabilities:** - Probability Xavier solves: $P(X) = \frac{1}{4}$ - Probability Yvonne solves: $P(Y) = \frac{1}{2}$ - Probability Zelda solves: $P(Z) = \frac{5}{8}$ 3. **Important rule:** Since the attempts are independent, the probability that multiple independent events all occur is the product of their individual probabilities. 4. **Calculate the probability that Zelda does NOT solve the problem:** $$P(\text{Zelda fails}) = 1 - P(Z) = 1 - \frac{5}{8} = \frac{3}{8}$$ 5. **Calculate the combined probability:** $$P(X \text{ and } Y \text{ and not } Z) = P(X) \times P(Y) \times P(\text{Zelda fails}) = \frac{1}{4} \times \frac{1}{2} \times \frac{3}{8}$$ 6. **Simplify:** $$= \frac{1 \times 1 \times 3}{4 \times 2 \times 8} = \frac{3}{64}$$ 7. **Final answer:** The probability that Xavier and Yvonne solve the problem but Zelda does not is $\boxed{\frac{3}{64}}$. This corresponds to option E.