Question

In: Statistics and Probability

Ontario Gateway Airlines’ first-class cabin has 10 seats in each plane. Ontario’s overbooking policy is to...

Ontario Gateway Airlines’ first-class cabin has 10 seats in each plane. Ontario’s overbooking policy is to sell up to 11 first class tickets since cancellations and no-shows are always possible (and indeed are quite likely).

For a given flight on Ontario Gateway, there were 11 first class tickets sold. Suppose that each of the 11 persons who purchased tickets has a 20% chance of not showing up for the flight and that the likelihood of different persons showing up for the flight is independent. The money for tickets to the passengers who didn't show up is returned.

(a) What is the probability that at most 5 of the 11 persons who purchased first class tickets show up for the flight?

(b) what is the probability that exactly 10 of the persons who purchased first class tickets show up for the flight?

(c) Thus, for example, if 10 of the first class passengers show up for the flight, the airline’s profit is $12,000. If 11 first class passengers show up, the profit is $9,000. What is the expected profit from first-class passengers for this flight?

(d) suppose that only 10 first class tickets had been sold. What would be the expected profit from first-class passengers for this flight?

(e) People often travel in groups of two or more. Does this affect the independence assumption about passenger behaviour? Why or why not?

Solutions

Expert Solution

The random variable representing the number of passengers who arrive out of 11 follows Binomial distribution with
The PMF of is

a) The probability that at most 5 of the 11 persons who purchased first class tickets show up for the flight is

R command below:
> pbinom(5,11,0.8)
[1] 0.01165421
b)  The probability that exactly 10 of the persons who purchased first class tickets show up for the flight is

R command below:

> dbinom(10,11,0.8)
[1] 0.2362232

c) The probability 10 or less of the first class passengers show up for the flight is

The probability that 11 first class passengers show up is

The expected profit from first-class passengers for this flight is

d) As given in part (c) of the question, the expected profit is

orchestra answered 2 years ago
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