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JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then \[P(X=1)\] is                                 [AIEEE 2003]

    A)                 1/32       

    B)                 1/16

    C)                 1/8         

    D)                 ¼

    Correct Answer: A

    Solution :

               \[\left. \begin{matrix}    np=4  \\    npq=2  \\ \end{matrix} \right\}\,\Rightarrow \,q=\frac{1}{2},\,p=\frac{1}{2},\,n=8\]                 \[P\,(X=1)={{\,}^{8}}{{C}_{1}}\left( \frac{1}{2} \right)\,\,\,{{\left( \frac{1}{2} \right)}^{7}}\]\[=8.\,\frac{1}{{{2}^{8}}}=\frac{1}{{{2}^{5}}}=\frac{1}{32}\].


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