6 In their football matches, Rovers score goals independently and at random times. Their average rate of scoring is 2.3 goals per match.
- State the expected number of goals that Rovers will score in the first half of a match.
- Find the probability that Rovers will not score any goals in the first half of a match but will score one or more goals in the second half of the match.
- Football matches last for 90 minutes. In a particular match, Rovers score one goal in the first 30 minutes. Find the probability that they will score at least one further goal in the remaining 60 minutes.
Independently of the number of goals scored by Rovers, the number of goals scored per football match by United has a Poisson distribution with mean 1.8.
- Find the probability that a total of at least 3 goals will be scored in a particular match when Rovers play United.