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JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    The probability of hitting a target by three marksmen are \[\frac{1}{2},\,\frac{1}{3}\] and \[\frac{1}{4}\] respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is                                             [AI CBSE 1982]

    A)                 \[\frac{11}{24}\]  

    B)                 \[\frac{1}{12}\]

    C)                 \[\frac{1}{8}\]       

    D)                 None of these

    Correct Answer: A

    Solution :

               Here \[P(A)=\frac{1}{2},\] \[P(B)=\frac{1}{3},\] \[P(C)=\frac{1}{4}\]            Hence required probability                 \[=P(A)P(\bar{B})P(\bar{C})+P(\bar{A})P(B)P(\bar{C})+P(\bar{A})P(\bar{B})P(C).\]


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