Suppose that X has Poisson distribution. If $P(X=2)=\frac{2}{3} P(X=1)$, then $P(X=0)$ is equal to

$e^{\frac{4}{3}}$ $e^{-1}$ $e^{\frac{-4}{3}}$ $e^{\frac{-3}{4}}$

$e^{\frac{-4}{3}}$

The correct answer is Option (3) → $e^{\frac{-4}{3}}$