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AP EAMCET · Maths · Probability

In a binomial distribution, if \(\mathrm{n}=4\) and \(\mathrm{P}(\mathrm{X}=0)=\frac{16}{81}\), then \(\mathrm{P}(\mathrm{X}=4)=\)

  1. A \(\frac{1}{8}\)
  2. B \(\frac{1}{27}\)
  3. C \(\frac{1}{16}\)
  4. D \(\frac{1}{81}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{81}\)

Step-by-step Solution

Detailed explanation

\(P(X=0) = \binom{n}{0} p^0 (1-p)^{n-0} \) \(\frac{16}{81} = \binom{4}{0} p^0 (1-p)^{4}\) \(\frac{16}{81} = (1-p)^4 \) \(1-p = \sqrt[4]{\frac{16}{81}} = \frac{2}{3}\) \(p = 1 - \frac{2}{3} = \frac{1}{3}\) \(P(X=4) = \binom{4}{4} p^4 (1-p)^{4-4}\)…