JEE Main & Advanced JEE Main Paper (Held on 09-4-2019 Morning)

  • 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) \[\frac{7}{32}\]

    Correct Answer: C

    Solution :

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

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