The probability distribution function for random variable $x$ in Poisson distribution is given by $P\left(X=x\right)=\frac{e^{-\lambda }{\lambda }^x}{x!} .....\left(1\right)$

Where the value of $x$ represents the number of events within the period, $\lambda$ is the average rate of events within the time period.

We know that the time period is infinity for Poisson distribution.

$\lambda$ is the product of the probability of success $p$ and the number of events $n$. So  $\lambda =np$

$\lambda =np=2000\times 0.0001=2$

Now put all values in $\left(1\right)$,

$P\left(X=3\right)=\frac{e^{-2}{2}^3}{3!}=\frac{4}{3e^2}$