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AP EAMCET · Maths · Probability

The number of trials conducted in a binomial distribution is 6. If the difference between the mean and variance of this variate is \(\frac{27}{8}\), then the probability of getting atmost 2 successes is

  1. A \(\frac{106}{4^6}\)
  2. B \(\frac{144}{4^6}\)
  3. C \(\frac{126}{4^6}\)
  4. D \(\frac{154}{4^6}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{154}{4^6}\)

Step-by-step Solution

Detailed explanation

\(n = 6\) \(\mu - \sigma^2 = np - npq = np(1-q) = np^2\) \(np^2 = \frac{27}{8}\) \(6p^2 = \frac{27}{8}\) \(p^2 = \frac{27}{48} = \frac{9}{16}\) \(p = \frac{3}{4}\) \(q = 1 - p = 1 - \frac{3}{4} = \frac{1}{4}\) \(P(X \le 2) = P(X=0) + P(X=1) + P(X=2)\)…