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If the mean and the variance of a binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to

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If the mean and the variance of a binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to: A. 2/3 B. 4/5 C. 7/8 D. 15/16 Select the correct answer from above options

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Correct Answer - D Let n and p be the parameters of the binomial distribution. Then, np=2andnpq=1 ⇒q= 1 2 ,p= 1 2 andn=4 [Given] ∴P(X≥1)=1-P(X<1)=1-P(X=0) ⇒P(X≥1)-.Nc0p0qn-0=1-.4C0×( 1 2 )4= 15 16

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