Probability, Statistics

Question

Can anyone please help me with the problem given below.

If you receive on average 2 spam emails per day, what is the probability that you receive at most 2 spam emails on a given day?

Thanks in advance.

Answer 1

Note: $X\sim P(2)$. The required probability is: $$P(X\le 2)=P(X=0)+P(X=1)+P(X=2)=\\ \frac{2^0\cdot e^{-2}}{0!}+\frac{2^1\cdot e^{-2}}{1!}+\frac{2^2\cdot e^{-2}}{2!}=0.6767.$$