Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

In a college, each student selects just one sport from tennis, hockey or netball. The table gives the numbers of Year 1 and Year 2 students at the college who play each sport. One student is selected at random from the 120 students. The events $X$ and $N$ are defined as follows: $X$: the student is in Year 1. $N$: the student plays netball.
(a)[1]

Find the value of $P(X \mid N)$.

(b)[1]

Find the value of $P(N \mid X)$.

(c)[1]

Determine whether $X$ and $N$ are independent events.

(d)[3]

One student who plays netball takes 8 shots at goal. For each shot, the probability that she succeeds is $0.15$, independently of the other shots. Find the probability that she succeeds on fewer than 3 of these shots.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: $P(X\mid N)=\frac{12}{40}$ (or equivalent such as $\frac{3}{10},\ 0.3$)

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