6
$\begingroup$

I have this problem to solve:

Hockey teams 1 and 2 score goals at times of Poisson process with rates 1 and 2. Suppose that $N_1(0)=3$ and $N_2(0)=1$. What is the probability that $N_1(t)$ will reach 5 before $N_2(t)$ does?

I've re-worded this to: What is the prob that in the next 5 goals at least 2 of them are scored by team 1?

The only problem I have is finding out the probability of team one scoring a goal. Can we use the rates to work this out?

3 Answers 3