In a binomial distribution, if E(X)=40 and V(X)=8 , then the value of…

The correct answer is Option (1) → \(\displaystyle\frac{8}{5^{48}}\)

For a binomial distribution, mean = np and variance = npq:

    \(np = 40,\quad npq = 8\)

Dividing:

    \( \displaystyle q = \frac{8}{40} = \frac{1}{5},\quad p = \frac{4}{5} \)

    \( \displaystyle n = \frac{40}{p} = 40\times\frac{5}{4} = 50 \)

Then

    \( \displaystyle P(X=1) = {}^{50}C_{1}\left(\frac{4}{5}\right)\left(\frac{1}{5}\right)^{49} \)

    \( \displaystyle = \frac{50\times 4}{5^{50}} = \frac{200}{5^{50}} = \frac{8\times 25}{5^{50}} = \frac{8}{5^{48}} \)