2 A hotel chain has hotels in three types of location: city, coastal and country. The percentages of the chain's reservations for each of these locations are 30,55 and 15 respectively.
Each of the chain's hotels offers three types of reservation: Bed \& Breakfast, Half Board and Full Board.
The percentages of these types of reservation for each of the three types of location are shown in the table.
| \multirow{2}{*}{} | Type of location |
| | City | Coastal | Country |
| \multirow{3}{*}{Type of reservation} | Bed \ | Breakfast | 80 | 10 | 30 |
| Half Board | 15 | 65 | 50 |
| Full Board | 5 | 25 | 20 |
For example, 80 per cent of reservations for hotels in city locations are for Bed \& Breakfast.
- For a reservation selected at random:
- show that the probability that it is for Bed \& Breakfast is 0.34 ;
- calculate the probability that it is for Half Board in a hotel in a coastal location;
- calculate the probability that it is for a hotel in a coastal location, given that it is for Half Board.
- A random sample of 3 reservations for Half Board is selected.
Calculate the probability that these 3 reservations are for hotels in different types of location.