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AP EAMCET · Maths · Probability

A random variable X follows a binomial distribution in which the difference between its mean and variance is 1. If \(2 \mathrm{P}(\mathrm{x}=2)=3 \mathrm{P}(\mathrm{x}=1)\), then \(\mathrm{n}^2 \mathrm{P}(\mathrm{x}>1)=\)

  1. A \(13\)
  2. B \(11\)
  3. C \(15\)
  4. D \(12\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(11\)

Step-by-step Solution

Detailed explanation

\( np - np(1-p) = 1 \Rightarrow np^2 = 1 \) \( 2\binom{n}{2}p^2(1-p)^{n-2} = 3\binom{n}{1}p(1-p)^{n-1} \) \( n(n-1)p^2(1-p)^{n-2} = 3np(1-p)^{n-1} \) \( (n-1)p = 3(1-p) \Rightarrow np - p = 3 - 3p \Rightarrow np + 2p = 3 \)…