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JEE Main & Advanced Mathematics Probability Question Bank Odds in favour and odds against Addition theorem on probability

  • question_answer
    In two events \[P(A\cup B)=5/6\], \[P({{A}^{c}})=5/6\], \[P(B)=2/3,\] then A and B are                                         [UPSEAT 2001]

    A)                 Independent         

    B)                 Mutually exclusive

    C)                 Mutually exhaustive             

    D)                 Dependent

    Correct Answer: B

    Solution :

                       \[P(A{{}^{c}})=1-P(A)\] \[\Rightarrow \] \[P(A)=\frac{1}{6}\]                    Now \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]                    Þ  \[\frac{5}{6}=\frac{1}{6}+\frac{2}{3}-P(A\cap B)\] Þ  \[P(A\cap B)=0\]                                 Hence, events A and B are mutually exclusive.


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