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  4. Four persons can hit a target correctly with probabilities (1/2), (1/3), (1/4) and (1/8) respectively. if all hit at the target independently, then the probability that the target would be hit, is

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

JEE MainJEE Main 2019Probability - Part 2

Solution:

Let persons be $A,B,C,D$
P(Hit) = 1 - P(none of them hits)
$= 1 - P(\bar{A} \cap \bar{B} \cap \bar{C} \cap \bar{D})$
$1-P ((\bar{A}).P(\bar{B}).P(\bar{C}).P(\bar{D})$
$= 1 - \frac{1}{2}. \frac{2}{3}. \frac{3}{4}. \frac{7}{8}$
$= \frac{25}{32}$