3. In a company the 200 employees are classified as full-time workers, part-time workers or contractors.
The table below shows the number of employees in each category and whether they walk to work or use some form of transport.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Walk | Transport |
| Full-time worker | 2 | 8 |
| Part-time worker | 35 | 75 |
| Contractor | 30 | 50 |
The events \(F , H\) and \(C\) are that an employee is a full-time worker, part-time worker or contractor respectively. Let \(W\) be the event that an employee walks to work.
An employee is selected at random.
Find
- \(\mathrm { P } ( H )\)
- \(\mathrm { P } \left( [ F \cap W ] ^ { \prime } \right)\)
- \(\mathrm { P } ( W \mid C )\)
Let \(B\) be the event that an employee uses the bus.
Given that \(10 \%\) of full-time workers use the bus, \(30 \%\) of part-time workers use the bus and \(20 \%\) of contractors use the bus, - draw a Venn diagram to represent the events \(F , H , C\) and \(B\),
- find the probability that a randomly selected employee uses the bus to travel to work.