Let $X$ equal the number of alpha particle emissions of carbon-14 that are counted by a Geiger counter each second. Assume that the distribution of $X$ is Poisson with mean $16$. Let $W$ equal the time in seconds before the seventh count is made.
(a) Give the distribution of $W$.
(b) Find $\Pr(W \le 0.5)$. Hint: Use Equation 3.2-1 with $\lambda w = 8$.
I got and understood part a (I think), however for part b I am a bit confused as to why you would have to solve for both $\Pr(N=7)$ and $\Pr(N=8)$. For this you would just do $1 - e^{-\lambda}\frac{\lambda^n}{n!}$, correct?