4. The employees of a company are classified as management, administration or production. The following table shows the number employed in each category and whether or not they live close to the company or some distance away.
| Live close | |
| Management | 6 | 14 |
| Administration | 25 | 10 |
| Production | 45 | 25 |
An employee is chosen at random.
Find the probability that this employee
- is an administrator,
- lives close to the company, given that the employee is a manager.
Of the managers, \(90 \%\) are married, as are \(60 \%\) of the administrators and \(80 \%\) of the production employees.
- Construct a tree diagram containing all the probabilities.
- Find the probability that an employee chosen at random is married.
An employee is selected at random and found to be married.
- Find the probability that this employee is in production.