Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A box has $5$ discs, labelled $1$, $2$, $4$, $6$, $7$. William chooses $3$ discs at random, without replacement, and records the numbers written on them.
(i)[3]
Find the probability that the $3$ disc numbers consist of two even numbers and one odd number.
(ii)[5]
Let the random variable $S$ represent the smallest number among the $3$ discs chosen. Use a list of all possible selections ($126$, $246$ and so on) to construct the probability distribution table for $S$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid method for finding $P(\text{2 Es and 1 O})$, for example $\tfrac35\times\tfrac24\times\tfrac23\times{}^3C_2$ or an equivalent combinations approach” …