4 A survey of the 640 properties on an estate was undertaken. Part of the information collected related to the number of bedrooms and the number of toilets in each property.
This information is shown in the table.
| \multirow{2}{*}{} | Number of toilets | |
| | 1 | 2 | 3 | 4 or more | Total |
| \multirow{5}{*}{Number of bedrooms} | 1 | 46 | 14 | 0 | 0 | 60 |
| 2 | 24 | 67 | 23 | 0 | 114 |
| 3 | 7 | 72 | 99 | 16 | 194 |
| 4 | 0 | 19 | 123 | 48 | 190 |
| 5 or more | 0 | 0 | 11 | 71 | 82 |
| Total | 77 | 172 | 256 | 135 | 640 |
- A property on the estate is selected at random.
Find, giving your answer to three decimal places, the probability that the property has:
- exactly 3 bedrooms;
- at least 2 toilets;
- exactly 3 bedrooms and at least 2 toilets;
- at most 3 bedrooms, given that it has exactly 2 toilets.
- Use relevant answers from part (a) to show that the number of toilets is not independent of the number of bedrooms.
- Three properties are selected at random from those on the estate which have exactly 3 bedrooms.
Calculate the probability that one property has 2 toilets, one has 3 toilets and the other has at least 4 toilets. Give your answer to three decimal places.