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JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1, is

    A)                 \[\frac{2}{3}\]       

    B)                 \[\frac{4}{5}\]

    C)                 \[\frac{7}{8}\]       

    D)                 \[\frac{15}{16}\]

    Correct Answer: D

    Solution :

               We have mean \[(X)=np=2\]                   and variance \[(X)=npq=1\] Þ \[q=\frac{1}{2}\] or \[p=\frac{1}{2}\]                   and \[n=4\]                 Thus \[p(X\ge 1)=1-p(X=0)=1-{}^{4}{{C}_{0}}{{\left( \frac{1}{2} \right)}^{4}}=\frac{15}{16}\].


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