"Grand Salami" Goal Distribution

[calmB4storm]

Let's take an simplified example first, with three hypothetical hockey games. Let's say the first game has an average expectation of 4 total goals, the second game has an average expectation of 5 total goals, and the third game has an average expectation of 6 total goals. Assuming that the Poisson distribution is an accurate model of each game's total goals (btw, is this a safe assumption to make?), how would I determine the probability that the combined total of the three games is greater than, say, 13?

Also, would I be able to use the same technique to go about solving more complex problems (like ten games instead of just three)?

Thanks,
calm

[DrVanNostrin]

The total number of goals scored in the 3 games should follow a poisson(15) distribution. (Think about where a poisson distibution comes from.)