Poisson Distribution Word Problem

Question

The image you are looking is a solution to a problem that has been cropped out. I'm certain the solution is incorrect since it does not include P(X=2). Just to be on the overly safe side, I decided to verify this on stack exchange. I got an answer of roughly 0.55.

Answer 1

The solution is correct. It does not include $P(X = 2)$ because the question asks what the probability that there are at least two flaws in a tape is. This is equivalent to $P(X \geq 2)$, as denoted in the solution. You do not include two because, as the solution shows, $$P(X\geq 2) = 1- [(P(X=0) + P(X=1)] $$ the two other cases in the Poisson process. You would include $P(X=2)$ in the terms subtracted were the question asking what the probability was that there were more than two flaws in a tape.

Answer 2

"At least two" means the same as "neither zero nor one". That means the easiest way to calculate the probability is to calculate the probability of "either zero or one" and reverse it. There is no need to include the calculation of $P(X=2)$.