Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
On each day, Annabel chooses rice, potato or pasta to eat. For each option, independently, the chance that she eats rice is $0.75$, the chance that she eats potato is $0.15$ and the chance that she eats pasta is $0.1$.
(i)[2]
Calculate the probability that, over a week of $7$ days, Annabel eats pasta on exactly $2$ days.
(ii)[3]
Calculate the probability that, during a stretch of $5$ days, Annabel eats rice on $2$ days, potato on $1$ day and pasta on $2$ days.
(iii)[5]
Calculate the probability that Annabel eats potato on more than $44$ days in a year of $365$ days.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply binomial term $^{7}C_2 p^2(1-p)^5$” …