1. **Stating the problem:** We have two shooters, John and Santana. - Probability John hits the target: $P(J) = \frac{3}{10}$ - Probability Santana hits the target: $P(S) = \frac{2}{15}$ We want to find: - Probability neither hits the target - Probability at least one hits the target - Probability exactly one hits the target 2. **Calculate probability neither hits the target:** The probability John misses is $1 - P(J) = 1 - \frac{3}{10} = \frac{7}{10}$. The probability Santana misses is $1 - P(S) = 1 - \frac{2}{15} = \frac{13}{15}$. Since they shoot independently, the probability neither hits is: $$P(\text{neither}) = \frac{7}{10} \times \frac{13}{15} = \frac{91}{150}$$ 3. **Calculate probability at least one hits the target:** This is the complement of neither hitting: $$P(\text{at least one}) = 1 - P(\text{neither}) = 1 - \frac{91}{150} = \frac{59}{150}$$ 4. **Calculate probability exactly one hits the target:** This means either John hits and Santana misses, or Santana hits and John misses: $$P(\text{exactly one}) = P(J) \times (1 - P(S)) + (1 - P(J)) \times P(S)$$ Substitute values: $$= \frac{3}{10} \times \frac{13}{15} + \frac{7}{10} \times \frac{2}{15} = \frac{39}{150} + \frac{14}{150} = \frac{53}{150}$$ **Final answers:** - Probability neither hits: $\frac{91}{150}$ - Probability at least one hits: $\frac{59}{150}$ - Probability exactly one hits: $\frac{53}{150}$