Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

A fair 5-sided spinner is numbered $1, 2, 3, 4, 5$ on its faces. It is spun again and again until the side showing $2$ appears on the face where the spinner lands. The random variable $X$ represents how many spins are needed.
(a)[1]

Find the value of $P(X = 4)$.

(b)[2]

Find the value of $P(X < 6)$.

(c)[3]

Two fair 5-sided spinners, each labelled $1, 2, 3, 4, 5$, are spun at the same time. If the two results are the same, the score is $0$. If they are different, the score is the larger number minus the smaller number. Find the probability that the score is greater than $0$ given that the score is not equal to $2$.

(d)[3]

The two spinners are spun together repeatedly. For $9$ randomly selected spins of the pair, find the probability that the score is greater than $2$ on at least $3$ occasions.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Compute $P(X=4)$ from $(0.8)^3(0.2)$ to get $\frac{64}{625}$.” …

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