Question

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 115 passengers. The probability that a passenger does not show up is 0.05, and the passengers behave independently.

(a) Define X as the number of passenger showing up among 125 passengers. Give the probability mass function of X.

(b) What is the probability that every passenger who shows up can take the flight, i.e.P (X ≤ 115)?

(c) What is the expected number of passengers who will show up among 125 passengers, i.e.E(X)?

Answer 1

The probability that a randomly selected passenger will show up = 1 - 0.05 = 0.95

a) Let X denotes the number of passengers who will show up among 125 passengers who bought tickets.

X ~ Binomial (n = 125, p = 0.95)

The probability mass function of X is

b) The probability that every passenger who shows up can take the flight

c) The expected number of passengers who will show up among 125 passengers

= E(X)

= 125*0.95

= 118.75