Question

Premier League winner Manchester City averaged 2.5 goals last season. Assume that the number of goals Manchester City scores in a soccer match can be modeled by a Poisson distribution. a) What is the probability that Manchester City scores precisely 2 goals in their next match? b) Manchester City's leading scorer Erling Haaland scored a record 1.03 goals per match last season. Define a 'hat trick' when a player scores at least 3 goals in one match. What is the probability that Haaland scores a hat trick in the next match if we assume that the number of goals Haaland scores is Poisson? c) Given that Haaland has already scored a goal at halftime, what is the probability that he will finish the match with a hat trick? d) Now consider another scenario. Suppose that Manchester City scores 4 goals in a match. In this scenario, what is the probability that Erling Haaland scores a hat trick?

          Premier League winner Manchester City averaged 2.5 goals last season. Assume that the number of goals Manchester City scores in a soccer match can be modeled by a Poisson distribution.

a) What is the probability that Manchester City scores precisely 2 goals in their next match? 

b) Manchester City's leading scorer Erling Haaland scored a record 1.03 goals per match last season. Define a 'hat trick' when a player scores at least 3 goals in one match. What is the probability that Haaland scores a hat trick in the next match if we assume that the number of goals Haaland scores is Poisson?

c) Given that Haaland has already scored a goal at halftime, what is the probability that he will finish the match with a hat trick?

d) Now consider another scenario. Suppose that Manchester City scores 4 goals in a match. In this scenario, what is the probability that Erling Haaland scores a hat trick?

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