5.81 English Premier League Goals. The total number of goals scored per soccer match in the English Premier League (EPL) often follows the Poisson distribution. In one recent season, the average number of goals scored per match (over 380 games played) was 2.768. Compute the following probabilities.

1. (a) What is the probability that three or more goals are scored in a game?

2. (b) What is the probability that a game will end in a 0−0 tie?

3. (c) Explain why you cannot compute the probability that a game will end in a 1−1 tie but can provide an upper bound on this probability.