If a random variable X sim Bleft(n=5, p=frac{ | vedclass

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(B) Given that $X$ follows a binomial distribution $B(n, p)$ with $n=5$ and $p=\frac{1}{3}$.Since $q = 1 - p$,we have $q = 1 - \frac{1}{3} = \frac{2}{

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$\frac{40}{243}$

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(B) Given that $X$ follows a binomial distribution $B(n, p)$ with $n=5$ and $p=\frac{1}{3}$.Since $q = 1 - p$,we have $q = 1 - \frac{1}{3} = \frac{2}{3}$.The probability mass function is given by $P(X=k) = { }^n C_k p^k q^{n-k}$.We need to find $P(2 Substituting the values into the formula:$P(X=3) = { }^5 C_3 \left(\frac{1}{3}ight)^3 \left(\frac{2}{3}ight)^{5-3}$$P(X=3) = \frac{5 	imes 4}{2 	imes 1} 	imes \left(\frac{1}{27}ight) 	imes \left(\frac{2}{3}ight)^2$$P(X=3) = 10 	imes \frac{1}{27} 	imes \frac{4}{9}$$P(X=3) = \frac{40}{243}$

If a random variable $X \sim B\left(n=5, p=\frac{1}{3}\right)$,then $P(2 < X < 4) = $

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