Answer :

Correct answer is : 0.18

Prob(X = 1) = Prob(X = 2)

e = 2.718

$\frac{e^{-\lambda }{\lambda }^1}{1!}=\frac{e^{-\lambda }{\lambda }^2}{2!}$

λ = λ²/2

(λ² - 2λ) = 0 ⇒ λ (λ - 2) = 0

Since λ is always greater than zero, hence

λ - 2 = 0 ⇒ λ = 2

Prob(X = 3) = $\frac{e^{-\lambda }{\lambda }^3}{3!}=\frac{e^{-2}.2^3}{2\times 3}$

Prob(X = 3) = $\frac{8}{6.e^2}$ = 0.18