QUESTION 3 Suppose there are two football teams A and B. In recent matches Team A has a mean of 1 goal per match and Team B has a mean of 2 goals per match. Suppose that the probability of the number of goals scored by a team obeys a Poisson Distribution In the following questions, give the reasoning behind your answers. You can express some answers in terms of logarithms. Q 3(a) What is the probability of a draw? You can give your answer to 2 decimal places. Q 3(b) If the two teams play each other repeatedly, what is the probability of there being at least 4 matches before the first draw? Q 3(c)

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QUESTION 3
Suppose there are two football teams A and B. In recent matches Team A has a
mean of 1 goal per match and Team B has a mean of 2 goals per match.
Suppose that the probability of the number of goals scored by a team obeys a
Poisson Distribution
In the following questions, give the reasoning behind your answers.
You can express some answers in terms of logarithms.
Q 3(a)
What is the probability of a draw? You can give your answer to 2 decimal places.
Q 3(b)
If the two teams play each other repeatedly, what is the probability of there being at
least 4 matches before the first draw?
Q 3(c)
In a particular match what is the probability of waiting at least 20 mins for the first
goal?
Transcribed Image Text:QUESTION 3 Suppose there are two football teams A and B. In recent matches Team A has a mean of 1 goal per match and Team B has a mean of 2 goals per match. Suppose that the probability of the number of goals scored by a team obeys a Poisson Distribution In the following questions, give the reasoning behind your answers. You can express some answers in terms of logarithms. Q 3(a) What is the probability of a draw? You can give your answer to 2 decimal places. Q 3(b) If the two teams play each other repeatedly, what is the probability of there being at least 4 matches before the first draw? Q 3(c) In a particular match what is the probability of waiting at least 20 mins for the first goal?
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