• # question_answer 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 Main 9-4-2019 Morning] A) $\frac{25}{192}$                              B) $\frac{1}{192}$C) $\frac{25}{32}$        D) $\frac{7}{32}$

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