1. **Problem Statement:** Find the probability of winning a prize in a lottery where there are 10 prizes and 30 blanks. 2. **Formula:** Probability of an event $E$ is given by $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Explanation:** Here, the favorable outcomes are winning a prize, which is 10. The total outcomes are the total tickets, which is prizes plus blanks: $10 + 30 = 40$. 4. **Calculation:** $$P(\text{winning a prize}) = \frac{10}{40} = \frac{1}{4}$$ 5. **Interpretation:** The probability of winning a prize is $\frac{1}{4}$. 6. **Check options:** None of the given options (a) $\frac{4}{7}$, (b) $\frac{13}{34}$, (c) $\frac{7}{12}$, (d) $\frac{2}{15}$ matches $\frac{1}{4}$. Possibly a misprint or different interpretation. 7. **Conclusion:** Based on standard probability calculation, the answer is $\frac{1}{4}$. **Final answer:** $\boxed{\frac{1}{4}}$