Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target…

Let probability of hitting target by $P$ is $E_1$ ,$Q$ is $E_2$ ,and by $R$ is $E_3$

From the question Required probability is $P\left(E_1\right)P\left(E_2\right)P\left(\overline{E_3}\right)+P\left(\overline{E_1}\right)P\left(E_2\right)P\left(\overline{E_3}\right)+P\left(E_1\right)P\left(\overline{E_2}\right)P\left(\overline{E_3}\right)$$=\left(\frac{3}{4}\right) \left(\frac{1}{2}\right) \left(\frac{3}{8}\right)+\left(\frac{1}{4}\right) \left(\frac{1}{2}\right)\left(\frac{3}{8}\right)+\left(\frac{3}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)$

$=\frac{12+9}{64}$

$=\frac{21}{64}$