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. Calculate the expected revenue of the tour operator.

• 955
• 962
• 967
• 976
• 985

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

The tour operator collects 21 x 50 = 1050 for the 21 tickets sold. The probability that all 21 passengers will show up is

(1 − 0.02 )21  = (0.98)21 = 0.65. 

Therefore, the tour operator’s expected revenue is

1050 – 100(065) = 985.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.