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JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    A and B are two independent events such that \[P(A)=1/2\]and\[P(B)=1/3\]. Then P (neither A nor B) is equal to                [J & K 2005]

    A)                 2/3         

    B)                 1/6

    C)                 5/6         

    D)                 1/3

    Correct Answer: D

    Solution :

               P (neither A nor B) = \[P(\bar{A}\cap \bar{B})\]= \[P(\bar{A})\,.\,P(\bar{B})\]            \[P(\bar{A})=1-P(A)\] = \[1-\frac{1}{2}=\frac{1}{2}\]            \[P(\bar{B})=1-P(B)=1-\frac{1}{3}=\frac{2}{3}\]                                 \[\therefore \] \[P(\bar{A}).P(\bar{B})=\frac{1}{2}\times \frac{2}{3}=\frac{1}{3}\].


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