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JEE Previous Year Question

$If the mean and variance of a binomial distribution are 4 and \frac{4}{3} respectively, then P (X = 2) =$

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $\frac{20}{243}$
B $\frac{40}{243}$
C $\frac{28}{729}$
D $\frac{8}{27}$

Correct answer: A

Solution

(a) We have, np = 4, npq = \frac{4}{3} Here, q = \frac{1}{3} \Rightarrow p = \frac{2}{3} and n = 6 Now, P (X = r) =^{n} C_{r} q^{n - r} p^{r} \Rightarrow P (X = 2) =^{6} C_{2} (\frac{1}{3})^{4} (\frac{2}{3})^{2} = \frac{20}{243}

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