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

Length of time employed, x years Female Male

x < 49 16

4 < or equal to x < 10 14 20

10 < or equal to x 7 24

One of the 90 administrators is selected at random.

(a) Find the probability that the administrator is female.

(b) Given that the administrator has been employed by the company for less than 4 years,

find the probability that this administrator is male.

(c) Given that the administrator has been employed by the company for less than 10

years, find the probability that this administrator is male.

(d) 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'.