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

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14.Probability

hard

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

$\frac{{21}}{{64}}$

$\frac{{9}}{{64}}$

$\frac{{15}}{{64}}$

$\frac{{39}}{{64}}$

(JEE MAIN-2017) (JEE MAIN-2013)

Solution

Required probability

$=\left(\frac{3}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)+\left(\frac{1}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)+\left(\frac{3}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)$

$=\frac{12+9}{64}=\frac{21}{64}$

Standard 11

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Solution

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