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JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    A die is tossed thrice. If getting a four is considered a success, then the mean and variance of the probability distribution of the number of successes are         [DSSE 1987]

    A)                 \[\frac{1}{2},\,\frac{1}{12}\]              

    B)                 \[\frac{1}{6},\,\frac{5}{12}\]

    C)                 \[\frac{5}{6},\,\frac{1}{2}\]

    D)                 None of these

    Correct Answer: D

    Solution :

               We are given that \[n=3,\] \[p=\frac{1}{6},\] \[q=\frac{5}{6}\]            Mean \[=np=3\times \frac{1}{6}=\frac{1}{2}\]                 Variance \[=nqp=3\times \frac{1}{6}\times \frac{5}{6}=\frac{5}{12}.\]


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