17 The number of toilets in each of a random sample of 200 properties from a town was recorded.
Four types of properties were included: terraced, semi-detached, detached and apartment.
The data is summarised in the table below.
| \multirow{2}{*}{} | Number of toilets |
| One | Two | Three |
| Terraced | 20 | 10 | 4 |
| Semi-Detached | 18 | 50 | 16 |
| Detached | 12 | 10 | 8 |
| Apartment | 22 | 30 | 0 |
One of the properties is selected at random.
\(A\) is the event 'the property has exactly two toilets'.
\(B\) is the event 'the property is detached'.
17
- Find \(\mathrm { P } ( A )\).
17
- (ii) Find \(\mathrm { P } \left( A ^ { \prime } \cap B \right)\).
17
- (iii) Find \(\mathrm { P } ( A \cup B )\).
17 - Determine whether events \(A\) and \(B\) are independent.
Fully justify your answer.
17 - Using the table, write down two events, other than event \(\boldsymbol { A }\) and event \(\boldsymbol { B }\), which are mutually exclusive.
Event 1 \(\_\_\_\_\)
\section*{Event 2}