Question

Three persons $P,Q$ and $R$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $P$ or $Q$ but not by $R$ is.

• A. $\frac{39}{64}$
• B. $\frac{21}{64}$
• C. $\frac{9}{64}$
• D. $\frac{15}{64}$

Answer 1

The correct option is B $\frac{21}{64}$

We have to find find probability when

P-hits
Q-hits
R-does not hits

$P{Q}^{\prime }{R}^{\prime }+P^{\prime }Q{R}^{\prime }+PQ{R}^{\prime }$

$=\frac{3}{4}\times \frac{1}{2}\times \frac{3}{8}+\frac{1}{4}\times \frac{1}{2}\times \frac{3}{8}+\frac{3}{4}\times \frac{1}{2}\times \frac{3}{8}$

$=\frac{9+3+9}{64}=\frac{21}{64}$.