Question

A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is 0.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 (ticket cost + 50 penalty) to the tourist. What is the expected revenue of the tour operator?

Answer 1

The expected revenue is $984.6.

Explanation:

The tourist operator sells 21 non-refundable tickets, as the tourist may not show up.

The tourist have a probability of 0.02 of not showing up, independent of each other.

The income is the selling of the 21 tickets at $50 each.

`I=21*50=1,050`

The only cost considered in this problem is the refund if a tourist show up and a seat is not available.

This only happens when the 21 tourists show up. If each tourist has a probability of 0.02 of not showing up, they have a probability of 0.98 of showing up.

For the event that the 21 tourists show up, we have the probability:

`P=0.98^(21)\approx0.654`

For each of this event, the tour operator has to pay $100, so the expected revenue of the tour operator is:

`E(R)=I-E(C)=1,050-0.654\cdot 100=1,050-65.4=984.6`