Question

Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is:

• A. $\frac{25}{32}$
• B. $\frac{1}{192}$
• C. $\frac{7}{32}$
• D. $\frac{25}{192}$

Answer 1

The correct option is A $\frac{25}{32}$

P(Hit)=1-P(none of them hit)
$=1-P(\overline{A}\cap \overline{B}\cap \overline{C}\cap \overline{D})=1-P\left(\overline{A}\right).P\left(\overline{B}\right).P\left(\overline{C}\right).P\left(\overline{D}\right)=1-\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \frac{7}{8}=1-\frac{7}{32}=\frac{25}{32}$