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

  • question_answer
    If \[P(A\cup B)=0.8\] and \[P(A\cap B)=0.3,\] then \[P(\bar{A})+P(\bar{B})=\] [EAMCET 2003]

    A)                 0.3         

    B)                 0.5

    C)                 0.7         

    D)                 0.9

    Correct Answer: D

    Solution :

                       \[P(A'\,\cap B')\,=1-P(A\cup B)\,=1-0.8=0.2\]                    \[P(A'\cup B')=1-P(A\cap B)=1-0.3=0.7\]                    \[P(A'\cup B')=P(A')\,+\,P(B')-P(A'\cap B')\]                                 Þ \[\,0.7\,=P(A')+P(B')-0.2\] Þ \[\therefore \].


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