Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The number of goals scored by a sports team during the first half of a match is modelled by $X \sim \text{Po}(3.1)$. The number of goals scored by the same team during the second half of a match is modelled by $Y \sim \text{Po}(2.4)$. You may assume that the distributions of $X$ and $Y$ are independent.
(a)[2]
Find $\text{P}(X < 4)$.
(b)[3]
Find the probability that, in a randomly chosen match, the team scores at least 5 goals.
(c)[4]
Given that the team scores a total of 5 goals in a randomly chosen match, find the probability that they score exactly 3 goals in the first half.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use an appropriate Poisson expression such as $e^{-3.1}\left(1+3.1+\dfrac{3.1^2}{2!}+\dfrac{3.1^3}{3!}\right)$ or an equivalent form.” …