JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-I

  • question_answer
    If 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) \[\frac{11}{16}\]

    Correct Answer: D

    Solution :

    [d] We hove; np =2=mean Npq=1=variance \[\Rightarrow p=\frac{1}{2};q=\frac{1}{2}\And n=4\] Required probability \[=P(x>1)\] \[=1-P(x\le 1)\] \[=1-[P(x=0)+P(x=1)]\] \[=1-{{[}^{4}}{{C}_{0}}{{q}^{4}}{{+}^{4}}{{C}_{1}}{{q}^{3}}{{p}^{1}}]\] \[=1-\frac{5}{16}=\frac{11}{16}\]


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