A credit card company mails out advertisements to prospective customers, and $0.4$% of these advertisements are returned to the company due to an incorrect or invalid address. If the company sends $250$ advertisements, find the probability that three will be returned.
I claim that this is a Poisson Process. Letting our mean be $(250)(0.004) = 1$, then plugging into the pmf formula gives $\frac {1}{6e}$. However, this was marked incorrect. I am not sure why this is the case but any insights would be greatly appreciated.
I suspect you are expected to model it as a binomial distribution, so the probability would be ${250 \choose 3}0.004^3\cdot 0.996^{247}\approx 0.0611894$, while $\frac 1{6e} \approx 0.061313$. I don't think your data is good enough to tell the difference between these.
Binomial is correct if you have a specific number of events with a given probability. Poisson is the limit of the binomial as the number of events goes to infinity, the probability of each event goes to zero, and the product is constant.