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AP EAMCET · Maths · Probability

If the mean and variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes of that binomial variate \(X\), is

  1. A \(\frac{1}{2}\)
  2. B \(\frac{219}{256}\)
  3. C \(\frac{37}{256}\)
  4. D \(\frac{7}{64}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{7}{64}\)

Step-by-step Solution

Detailed explanation

For a binomial distribution, Mean, \(\mu=n \rho=4\)... (i) Variance, \(\sigma^2=n \mathrm{p} q=2\)... (ii) On solving eqs. (i) and (ii), we get \(n=8, \mathrm{p}=\frac{1}{2}, q=\frac{1}{2}\) Probability of getting 2 successes,…