# Airline overbooking problem

• August 2nd 2009, 03:51 PM
morganfor
Airline overbooking problem
I'm having some trouble with this one:

An airline finds that 4 percent of the passengers that make reservations on a particular flight will not show up (not that each individual person has a 4 percent chance of showing up which is what is throwing me off). Consequently, their policy is to sell 100 reserved seats on a plane that only has 98 seats. Find the probability that ever person who shows up for the flight will find a seat available.
• August 2nd 2009, 04:44 PM
Random Variable
let X be the number of passengers that show up

X follows a binomial distribution with n= 100 and p = 0.96 (q=0.04)

we want $P(X \le 98) = 1- P(X \ge 99) =1 - \sum_{i=99}^{100} \binom{100}{i} (0.96)^{i}(0.04)^{i} \approx 0.913$