Four persons hit a target with probabilities 12,13,14,18.

Question

Four persons hit a target with probabilities $\dfrac12,\dfrac13,\dfrac14,\dfrac18$. Find the probability the target is hit.

Accepted Answer

$$P(\text{hit}) = 1-\left(1-\frac12\right)\left(1-\frac13\right)\left(1-\frac14\right)\left(1-\frac18\right) = 1-\frac12\cdot\frac23\cdot\frac34\cdot\frac78 = 1-\frac{7}{32}=\frac{25}{32}$$

Solutions · 1