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

  • question_answer
    The probabilities of occurrence of two events are respectively 0.21 and 0.49. The probability that both occurs simultaneously is 0.16. Then the probability that none of the two occurs is                                    [MP PET 1998]

    A)                 0.30       

    B)                 0.46

    C)                 0.14       

    D)                 None of these

    Correct Answer: B

    Solution :

                       \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]                    \[=0.21+0.49-0.16\Rightarrow P(A\cup B)=0.54\]                    Probability of none of two occurs                                 \[=1-P(A\cup B)=1-0.54=0.46.\]


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