Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
A factory produces a large quantity of ropes whose lengths are either $3\text{ m}$ or $5\text{ m}$. The number of ropes of length $3\text{ m}$ is four times the number of ropes of length $5\text{ m}$.
(i)[4]
A rope is selected at random. Find the expectation and variance of its length.
(ii)[2]
Two ropes are selected at random. Find the probability that their lengths are not the same.
(iii)[3]
Three ropes are selected at random. Find the probability that their combined length is $11\text{ m}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$P(3m)=\frac{4}{5}$ or $P(5m)=\frac{1}{5}$ shown or implied” …