# Poisson Distribution with two different expected value

Question:

Suppose there are number of accidents at location $A$ and location $B$ each day with Poisson Distribution with rate $0.001$ and the number of patients during each accident is Poisson distributed with rate $0.1$. Find the probability that the number of patients less than $3$ in one day.

Attempt:

So I did $E(N)=0.001\times 0.1=0.0001$ and then using this mean to find $$P(X<3)=\sum_{0}^{2}Poi(0.0001)$$

and I got a value of $1$. I am sure this is the wrong answer. I need some help. Thank you!