Statistics: How to use Poisson to determine if event would not occur?

Question

This is a follow up to my previous question

disk manufacturer averages 0.2 missing pulses per disk. let X denote # of missing pulses

I am using poisson distribution

I'm having trouble determining the probability that a disk would have no missing pulses

So I did P(X=0)$e^{-0.2}(0.2)^0 /0!$ = $0.81873$

So I think that is the probability of getting missing pulses so I did complement

$1-0.81873 = 0.18127$

another question asks me to determine the probability that next 2 disks will contain no missing pulses.

So I did 0.18127 * 0.18127 = 0.03285

Can anyone confirm if this is right?

Answer 1

Let $X$ be the number of missing pulses. As you wrote, $\Pr(X=0)=e^{-0.2}$. That is the answer, no further manipulation needed.

If $Y$ is the number of missing pulses on $2$ disks, then $Y$ has Poisson distribution with parameter $0.4$. So the probability of no missing pulses is $e^{-0.4}$.

For this particular problem, we could instead square the first answer, but it is important to get practice with the Poisson, to be able to handle more general problems.