1. **State the problem:** Bill spins two spinners, Spinner A with numbers $8, 4, 2, 1$ and Spinner B with numbers $7, 9, 5, 3$. He wins a prize if the sum of the numbers from both spinners is even. 2. **Formula and rules:** The probability of winning is the probability that the sum is even. Recall that the sum of two numbers is even if both numbers are even or both are odd. 3. **Identify even and odd numbers on each spinner:** - Spinner A: Even numbers = $8, 4, 2$, Odd number = $1$ - Spinner B: Odd numbers = $7, 9, 5, 3$ (all odd) 4. **Calculate probabilities:** - Probability Spinner A lands on even = $\frac{3}{4}$ - Probability Spinner A lands on odd = $\frac{1}{4}$ - Probability Spinner B lands on odd = $\frac{4}{4} = 1$ - Probability Spinner B lands on even = 0 5. **Sum is even if:** - Both numbers are even: Spinner A even and Spinner B even (impossible since Spinner B has no even numbers) - Both numbers are odd: Spinner A odd and Spinner B odd 6. **Calculate probability of sum even:** $$ P(\text{sum even}) = P(A \text{ odd}) \times P(B \text{ odd}) + P(A \text{ even}) \times P(B \text{ even}) $$ $$ = \frac{1}{4} \times 1 + \frac{3}{4} \times 0 = \frac{1}{4} $$ 7. **Final answer:** The probability that Bill wins a prize is $\boxed{\frac{1}{4}}$ or 0.25.