Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Bag $A$ has $4$ balls labelled $2, 4, 5, 8$. Bag $B$ has $5$ balls labelled $1, 3, 6, 8, 8$. Bag $C$ has $7$ balls labelled $2, 7, 8, 8, 8, 8, 9$. A single ball is chosen at random from each bag.
(i)[5]
Find the probability that exactly two of the chosen balls have the same number.
(ii)[2]
Given that exactly two of the selected balls have the same number, find the probability that both are numbered $2$.
(iii)[2]
Event $X$ means ‘exactly two of the chosen balls have the same number’. Event $Y$ means ‘the ball chosen from bag $A$ has number $2$’. With your working shown, determine whether events $X$ and $Y$ are independent or not.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Allow for combinations that involve at least two $2$s and $8$s” …