AP EAMCET · Maths · Probability
If the mean and variance of a binomial variate \(X\) are \(\frac{4}{3}, \frac{8}{9}\) respectively, then \(P(X=2)=\)
- A \(\frac{4}{27}\)
- B \(\frac{16}{81}\)
- C \(\frac{8}{27}\)
- D \(\frac{8}{81}\)
Answer & Solution
Correct Answer
(C) \(\frac{8}{27}\)
Step-by-step Solution
Detailed explanation
For a binomial variate x, From Eqs. \((i)\) and \((i i)\), we have \(q=\frac{2}{3}, p=\frac{1}{3}\) and \(n=4\) Now, \(P(X=2)={ }^4 C_2 p^2 q^2\) \[ =6\left(\frac{1}{3}\right)^2\left(\frac{2}{3}\right)^2=\frac{24}{81}=\frac{8}{27} \]
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