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

Question

Mathematics

Haley Wiggins

7 December, 03:17

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

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Laurel Roman · Answer 1

985

Step-by-step explanation:

Expected Value : If as per planning, only 20 tourists come up at booking of 21 people = per tourist ticket x 21 number of people : - 21 x 50 = 1050

Prob (a tourist coming) = 0.02, Prob (a tourist not coming) : - 1 - 0.02 = 0.98

Prob (21 tourists coming) = (0.98) ^21 = 0.654

Loss in this case = 100

So, expected revenue = 1050 - (0.654) 100

1050 - 65.4

= 984.6 = 985