Question

Every year on April 1, Anytown Tigers and Someville Lions play a soccer game. It is always a high-scoring game; the number of goals scored follows a Poisson
process with the average rate of one goal per 5 minutes. ( A soccer game consists of two halves, 45 minutes each. )

a) What is the probability that the fourth goal is scored during the last 10 minutes of
the first half?
b) What is the probability that the fifth goal is scored during the last 15 minutes of
the first half?
c) Find the probability that more than 20 goals are scored during the game. (Use Normal approximation.) Every year on A

Answer 1

a) p(3 goals in 35 minutes)*p(1 goal in 10 minutes)
b) Same sort of thing.
c) Average 18 / game.