Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

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) 2/3 (B) 4/5 (C) 7/8 (D) 15/16 - Mathematics

Question

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

• 2/3

• 4/5

• 7/8

• 15/16

Solution

15/16

Mean =2 and variance =1

$\Rightarrow np = 2 \text{ and npq } = 1$
$\Rightarrow q = \frac{1}{2}$
$\Rightarrow p = 1 - \frac{1}{2} = \frac{1}{2}$
$n = \frac{\text{ Mean} }{p}$
$\Rightarrow n = 4$
$\text{ Hence, the distribution is given by }$
$P\left( X = r \right) =^{4}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{4 - r} , r = 0, 1, 2, 3, 4$
$\therefore P(X \geq 1) = 1 - P(X = 0)$
$= 1 - \frac{1}{2^4}$
$= \frac{15}{16}$

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APPEARS IN

RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 12 | Page no. 28

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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) 2/3 (B) 4/5 (C) 7/8 (D) 15/16 Concept: Bernoulli Trials and Binomial Distribution.