Assume that the score in a soccer match follows a Poisson distribution, with Team A expected to score 1.35 goals in a particular game (lambda = 1.35). Given player X is expected to score 33% of Team A's goals and player Y is expected to score 25%, what is the probability that both players score in the game?
Sorry, I have tried these attempts- didn't want to put people off!
I tried using the binomial distribution given Team A has scored 1,2,3...etc. goals but it quickly became very complicated, especially as I wanted to extend this problem to 3 or more players. Also, I tried subtracting the null probabilities (i.e. player A doesn't score, player B doesn't score, both don't score) but there must be a related contingency given if one player scores then the probability of the other player scoring changes.
Please help!
