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JEE Main & Advanced JEE Main Online Paper (Held On 23 April 2013)

  • question_answer
                    A, B,C, try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are \[\frac{3}{4},\frac{1}{2},\frac{5}{8}.\] The probability that the target  is hit by A or B but not by C is :     JEE Main Online Paper ( Held On 23  April 2013 )

    A)                  \[21/64\]           

    B)                                         \[7/8\]

    C)                                         \[7/32\]                              

    D)                                         \[9/64\]

    Correct Answer: A

    Solution :

                      P(A or B but not by C) \[=P(A\cup B)\cap (\overline{C})\] \[=P(A\cup B)\times P(\overline{C})\] \[=P(A)+P(B)-P(A\cap B]\times P(\overline{C})\]= \[\left[ \frac{3}{4}+\frac{1}{2}-\frac{3}{4}\times \frac{1}{2} \right]\times \frac{3}{8}=\left( \frac{6+4-3}{8} \right)\times \frac{3}{8}=\frac{21}{64}\]


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