Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
A group of passengers is making the journey to Picton in a minibus. For each passenger, the probability of carrying a backpack is $0.65$, independent of the others. Each minibus has $12$ seats for passengers.
(i)[3]
Determine the probability that, on a full minibus travelling to Picton, the number of passengers carrying a backpack is between $8$ and $10$ inclusive.
(ii)[2]
Passengers board an empty minibus. Find the probability that the fourth passenger to board the minibus is the first one carrying a backpack.
(iii)[6]
Determine the probability that, in a random sample of $250$ full minibuses travelling to Picton, more than $54$ contain exactly $7$ passengers who are carrying backpacks.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate use of binomial probability terms, for example $^{12}C_8(0.65)^8(0.35)^4+^{12}C_9(0.65)^9(0.35)^3+^{12}C_{10}(0.65)^{10}(0.35)^2$” …