A tour operator offers a popular sight-seeing trip in a 20-seater bus. Based on past experiences, the operator estimates that there is a probability of 0.1 that an individual tourist will not show up, independent of other tourists. To increase his profits, he decides to take the risk and sell 22 tickets instead. If a tourist with a ticket shows up but the seat is not available, the tourist will be compensated. Assume that all tickets are sold out for each trip.

A tour operator offers a popular sight-seeing trip in a 20-seater bus. Based on past experiences, the operator estimates that there is a probability of 0.1 that an individual tourist will not show up, independent of other tourists. To increase his profits, he decides to take the risk and sell 22 tickets instead. If a tourist with a ticket shows up but the seat is not available, the tourist will be compensated. Assume that all tickets are sold out for each trip. (a) What is the probability that the operator will need to pay the compensation? (5 marks) (b) Given that each ticket costs $50 which is non-refundable and the compensation is $100, what is the expected revenue for each trip