A particular airline has a policy of routinely over - booking flights because pa

Question

A particular airline has a policy of routinely over - booking flights because past experience shows that some passengers fail to show. Here is a table with the number of passengers who cannot board the flight because there are more passengers than seats. What is the probability that a flight selected at random has the following passengers unable to find a seat: none? less than two? more than three? 2 and 4 What is the expected number of passengers who cannot board the flight due to over - booking? Interpret the expected value and explain why this airline has this policy

Explanation / Answer

1) P(None) = P(0) = 0.805

2) P(Less than two)

= P(0) + P(1)

= 0.805 + 0.113

= 0.918

3) P(More than three)

= P(4)

= 0.002

4) P(2 and 4)

= 0 (Because it is not possible that 2 and 4 passengers cant board flight simultaneously)

If it would be P(2 or 4) then:

P(2 or 4) = P(2) + P(4) = 0.057 + 0.002 = 0.059

5) Expected number of passengers who cannot board the flight due to over - booking

= 0(0.805) + 1(0.113) + 2(0.057) + 3(0.023) + 4(0.002)

= 0.304

6) Expected value interpretation:

On an average, 0.304 passengers will not be able to board the flight due to over - booking.

The reason of this policy can be explained from the expected value itself. The expected value is coming as 0.304 which is even less than 1. So. less than 1 passenger will not be able to board the flight due to over - booking. Since there is very low chance of seat unavailability due to overbooking, this policy will increase the airline's profit.

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