Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
Eli has four fair $4$-sided dice, each face labelled $1, 2, 3, 4$. He rolls all four together. The random variable $X$ stands for the number of $2$s that appear.
(a)[2]
Show that the value of $P(X = 3)$ is $\frac{3}{64}$.
(b)[2]
Complete the probability distribution table below for $X$.
(c)[2]
Find the value of $\mathrm{E}(X)$.
(d)[5]
Eli throws the four dice together on 96 separate occasions. Use an approximation to determine the probability that he gets at least two 2s on fewer than 20 of those occasions.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct probability expression is $\dfrac{3}{4}\left(\dfrac{1}{4}\right)^3\times4$.” …