What is the variance of the number of times a 6 appears when a fair die is rolled 10 times?

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What is the variance of the number of times a 6 appears when a fair die is rolled 10 times?

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Harper 1 week 2021-09-15T22:45:54+00:00 1 Answer 0

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    2021-09-15T22:47:29+00:00

    Answer: \dfrac{25}{18}

    Step-by-step explanation:

    In Binomial distribution ,

    The Formula to find Variance is given by :-

    \sigma^2=np(1-p) , where n = Total number of trials and p= probability of getting success in each trial.

    Total outcomes on a fair dice (1,2,3,4,5,6)= 6

    When we roll a fair dice, then the probability of getting a 6 =\dfrac{1}{6}

    [∵ Probability = \dfrac{\text{favorable outcomes}}{\text{Total outcomes}}]

    Then, the variance of the number of times a 6 appears when a fair die is rolled 10 times :-

    [ Here n= 10 and p=\dfrac{1}{6} ]

    \sigma^2=(10)\dfrac{1}{6}(1-\dfrac{1}{6})\\\\=(10)\dfrac{1}{6}\dfrac{5}{6}=\dfrac{25}{18}

    Hence, the variance of the number of times a 6 appears when a fair die is rolled 10 times= \dfrac{25}{18}

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