9709 P52 - Nov 2024 - Q1 - 6 marks
9760
At a college each student plays exactly one of tennis, hockey or netball. The numbers in Years 1 and 2 are shown below.
| Tennis | Hockey | Netball | |
|---|---|---|---|
| Year 1 | 16 | 22 | 12 |
| Year 2 | 24 | 18 | 28 |
One student is chosen at random from all 120. Let \(X\) be the event that the student is in Year 1 and \(N\) the event that the student plays netball.
(a) Find \(P(X\mid N)\). [1]
(b) Find \(P(N\mid X)\). [1]
(c) Determine whether X and N are independent. [1]
One netball player takes 8 shots at goal. Each shot succeeds with probability 0.15, independently of all other shots.
(d) Find the probability that she succeeds on fewer than 3 shots. [3]
