Poisson Distribution with two different expected value

#1
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)=\(\sum_{0}^{2}Poi(0.0001)=1\)

and I got a value of \(1\). I am sure this is the wrong answer. Where did it go wrong? I need some help. Thank you!
 

Mean Joe

TS Contributor
#2
First thing, I would ask you to double-check the question: Is the question asking for <3 patients in one day or in one year? Is that rate of 0.001 per day or per hour?