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JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is [CEE 1993; IIT Screening]

    A)                 0.25       

    B)                 0.21       

    C)                 0.16       

    D)                 0.6976

    Correct Answer: D

    Solution :

               Let \[{{p}_{1}}=0.4,\] \[{{p}_{2}}=0.3,\] \[{{p}_{3}}=0.2\] and \[{{p}_{4}}=0.1\]                    \[P\](the gun hits the plane) \[=P\] (the plane is hit in once)            \[=1-P\] (the plane is hit in none of the shots)                 \[=1-(1-{{p}_{1}})(1-{{p}_{2}})(1-{{p}_{3}})(1-{{p}_{4}})\]\[=0.6976\].


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