ABC Airlines' first class cabins have 10 seats in each plane. ABC'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 ABC Airlines, 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 light, and that the events that different persons show up for the flight are independent. (Please assume that there is no refund if the customer does not show up for the flight) (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 11 persons who purchased first class tickets show up for the flight? (c) Suppose that the cost of each first class ticket is $12,000. (Let's assume that this $12,000 contributes entirely to profit since the variable cost associated with a passenger on a flight is close to zero.) Suppose further that any overbooked seat costs the airline $30,000, which is the cost of the free ticket issued to the passenger plus some potential cost in damaged customer relations. (First class passengers do not expect to be bumped!) What is the expected profit from first class passengers for this flight? (d) Suppose that only 10 first class tickets were sold. What would be the expected profit from first class passengers for this flight? (e) If the probability of not showing up increases, ABC Airlines may even consider sell up t0 12 first class tickets. What is the minimum probability of not showing up that may drive ABC to make this decision?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Part D and E

ABC Airlines' first class cabins have 10 seats in each plane. ABC'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 ABC
Airlines, 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
light, and that the events that different persons show up for the flight are
independent. (Please assume that there is no refund if the customer does not
show up for the flight)
(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 11 persons who purchased
first class tickets show up for the flight?
(c) Suppose that the cost of each first class ticket is $12,000. (Let's assume
that this $12,000 contributes entirely to profit since the variable cost
associated with a passenger on a flight is close to zero.) Suppose further
that any overbooked seat costs the airline $30,000, which is the cost of the
free ticket issued to the passenger plus some potential cost in damaged
customer relations. (First class passengers do not expect to be bumped!)
What is the expected profit from first class passengers for this flight?
(d) Suppose that only 10 first class tickets were sold. What would be the
expected profit from first class passengers for this flight?
(e) If the probability of not showing up increases, ABC Airlines may even
consider sell up t0 12 first class tickets. What is the minimum probability
of not showing up that may drive ABC to make this decision?

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The number of times that a person contracts a cold in a given year is a Poisson random variable with parameter λ=5. Suppose that a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to λ=3 for 70 percent of the population. For the other 30 percent of the population, the drug has no appreciable effect on colds. If Peter tried the drug for a year and has 3 colds in that time, what is the probability that the drug is beneficial for him?

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