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

Options
  • 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.
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