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

  • question_answer
    If A and B are two events of a random experiment,                                                                                             \[P\,(A)=0.25\] ,                                                                                             \[P\,(B)=0.5\]  and                                                                                      \[P\,(A\cap B)=0.15,\]   then                                                                                      \[P\,(A\cap \bar{B})=\]                                                 [MP PET 1987]

    A)                 0.1         

    B)                 0.35

    C)                 0.15       

    D)                 0.6

    Correct Answer: A

    Solution :

                       Since                                                                        \[P(A\cap \bar{B})+P(A\cap B)=P(A)\]                                                                                                         \[\Rightarrow P(A\cap \overline{B})=P(A)-P(A\cap B)=0.25-0.15=0.1\]


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