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JEE Main & Advanced JEE Main Solved Paper-2017

  • question_answer
    For three events A, B and C, P(Exactly one of A or B occurs)= P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) \[=\frac{1}{4}\]and  P(All the three events occur simultaneously) \[=\frac{1}{16}.\] Then the probability that at least one of the  events occurs, is :-       JEE Main Solved Paper-2017

    A)  \[\frac{3}{16}\]                               

    B)  \[\frac{7}{32}\]

    C)  \[\frac{7}{16}\]                               

    D)  \[\frac{7}{64}\]

    Correct Answer: C

    Solution :

     P (exactly one of A or B occurs) \[=P(A)+P(B)-2P(A\cap B)=\frac{1}{4}\] P(Exactly one of B or C occurs) \[=P(B)+P(C)-2P(B\cap C)=\frac{1}{4}\] P(Exactly one of C or A occurs) \[=P(C)+P(A)-2P(C\cap A)=\frac{1}{4}\] Adding all, we get \[2\sum P(A)-2\sum P(A\cap B)=\frac{3}{4}\] \[\therefore \]\[\sum P(A)-\sum P(A\cap B)=\frac{3}{8}\] Now, \[P(A\cap B\cap C)=\frac{1}{16}\](given) \[\therefore \]  \[P(A\cup B\cup C)\] \[=\sum P(A)-\sum P(A\cap B)+P(A\cap B\cap C)\] \[=\frac{3}{8}+\frac{1}{16}=\frac{7}{16}\]


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