Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A box holds 2 green apples and 2 red apples. The apples are removed from the box one at a time, without replacement. The procedure ends once both red apples have been removed. The random variable $X$ represents the number of apples removed when the procedure ends.
(i)[3]
Show that $P(X = 3)$ is $\frac{1}{3}$.
(ii)[3]
Draw up the probability distribution table for $X$.
(iii)[5]
A different box contains $2$ yellow peppers and $5$ orange peppers. Three peppers are chosen at random from the box without replacement. Given that at least $2$ of the peppers chosen from the box are orange, find the probability that all $3$ peppers are orange.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Start from $P(X=3)=P(GRR)+P(RGR)$” …