1 At a college, the students choose exactly one of tennis, hockey or netball to play. The table shows the numbers of students in Year 1 and Year 2 at the college playing each of these sports.
| Tennis | Hockey | Netball |
| Year 1 | 16 | 22 | 12 |
| Year 2 | 24 | 18 | 28 |
One student is chosen at random from the 120 students. Events \(X\) and \(N\) are defined as follows:
\(X\) : the student is in Year 1
\(N\) : the student plays netball.
- Find \(\mathrm { P } ( X \mid N )\).
- Find \(\mathrm { P } ( N \mid X )\).
- Determine whether or not \(X\) and \(N\) are independent events.
One of the students who plays netball takes 8 shots at goal. On each shot, the probability that she will succeed is 0.15 , independently of all other shots. - Find the probability that she succeeds on fewer than 3 of these shots.