7 A travel agency in Tunisia offers customers a 3-day tour into the Sahara desert by either coach or minibus.
- The agency accepts bookings from 50 customers for seats on the coach. The probability that a customer, who has booked a seat on the coach, will not turn up to claim the seat is 0.08 , and may be assumed to be independent of the behaviour of other customers.
Determine the probability that, of the customers who have booked a seat on the coach:
- two or more will not turn up;
- three or more will not turn up.
- The agency accepts bookings from 15 customers for seats on the minibus. The probability that a customer, who has booked a seat on the minibus, will not turn up to claim the seat is 0.025 , and may be assumed to be independent of the behaviour of other customers.
Calculate the probability that, of the customers who have booked a seat on the minibus:
- all will turn up;
- one or more will not turn up.
- The coach has 48 seats and the minibus has 14 seats. If 14 or fewer customers who have booked seats on the minibus turn up, they will be allocated a seat on the minibus. If all 15 customers who have booked seats on the minibus turn up, one will be allocated a seat on the coach. This will leave only 47 seats available for the 50 customers who have booked seats on the coach.
Use your results from parts (a) and (b) to calculate the probability that there will be seats available on the coach for all those who turn up having booked such seats.
(4 marks)