Krzys’ Ostaszewski: http://www.krzysio.net
Author of the “Been There Done That!” manual for Course P/1
http://smartURL.it/krzysioP (paper) or http://smartURL.it/krzysioPe (electronic)
Instructor of online P/1 seminar: http://smartURL.it/onlineactuary
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May 2001 Course 1 Examination, Problem No. 37, also P Sample Exam Questions,
Problem No. 96, and Dr. Ostaszewski’s online exercise posted October 10, 2009
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?
A. 935
B. 950
C. 967
D. 976
E. 985
Solution.
The bus driver collects 21⋅ 50 = 1050 for the 21 tickets he sells. But he may have to
refund 100 to one passenger if all 21 ticket-holders show up. Since passengers are
independent of one another, 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 ⋅ 0.65 = 985.
Answer E.
© Copyright 2004-2009 by Krzysztof Ostaszewski.
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Exercises from the past actuarial examinations are copyrighted by the Society of
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