- A company employs 90 administrators. The length of time that they have been employed by the company and their gender are summarised in the table below.
| Length of time employed, \(x\) years | Female | Male |
| \(x < 4\) | 9 | 16 |
| \(4 \leqslant x < 10\) | 14 | 20 |
| \(10 \leqslant x\) | 7 | 24 |
One of the 90 administrators is selected at random.
- Find the probability that the administrator is female.
- Given that the administrator has been employed by the company for less than 4 years, find the probability that this administrator is male.
- Given that the administrator has been employed by the company for less than 10 years, find the probability that this administrator is male.
- State, with a reason, whether or not the event 'selecting a male' is independent of the event 'selecting an administrator who has been employed by the company for less than 4 years'.