Harvard and MIT will have a friendly hockey match. The number of goals that Harvard is expected to score follows a Poisson distribution with the average ₁ = 3 per game. On the other hand, the number of goals that MIT is expected to score follows a Poisson distribution with average ₂ = 4 per game.

a) What is the probability that MIT wins 2-1?

b) If the game becomes a 1-1 tie in the first half, what is the probability that Harvard wins 2-1?

c) What is the probability that the result at the end of the game is 2-2?

d) What is the probability that the result is a tie (with any result)?