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AP EAMCET · Maths · Probability

For a binomial variate \(X \sim B(n, p)\) the difference between the mean and variance is 1 and the difference between their squares is 11 . If the probability of \(P(x=2)=m\left(\frac{5}{6}\right)^n\) and \(n=36\) then \(m: n=\)

  1. A \(6: 5\)
  2. B \(7: 10\)
  3. C \(36: 1\)
  4. D \(42: 25\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(7: 10\)

Step-by-step Solution

Detailed explanation

Given that difference of mean variance is 1 \(\therefore n p-n p q=1 \Rightarrow n p(1-q)=1 \Rightarrow n p^2=1\) \(\qquad ....\mathrm{(i)}\) Also given \((n p)^2-(n p q)^2=11\) \(\qquad ....\mathrm{(ii)}\) \(n^2 p^2-n^2 p^2 q^2=11 \Rightarrow n^2 p^2\left(1-q^2\right)=11\)…