Question

Busy people arrive at the park according to a Poisson process with rate λ1=3/hour. Relaxed people arrive at the park according to an independent Poisson process with rate λ2=2/hour. Assume that no other people arrive at the park. During the last 10 minutes, exactly two people arrived at the park. What is the probability that they are both relaxed?

Answer 1

(2C2)*(2/(2+3))²=4/25