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

  • question_answer
    The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then \[P({A}')+P({B}')=\]

    A)                 0.9         

    B)                 1.15

    C)                 1.1         

    D)                 1.2

    Correct Answer: C

    Solution :

                       \[1-P({A}'\cap {B}')=0.6,\] \[P(A\cap B)=0.3,\] then                    \[P({A}'\cup {B}')=P({A}')+P({B}')-P({A}'\cap {B}')\]                    Þ \[1-P(A\cap B)=P({A}')+P({B}')-0.4\]                                 Þ \[P({A}')+P({B}')=0.7+0.4=1.1\].


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