# Probability Question

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• March 11th 2009, 03:16 AM
garrett88
Probability Question
Four percent of those who make an airline reservation do not show up for their flight. An airline sells 75 seats for a plane that has 73 seats (overbooking). What is the probability that every person who shows up will get a seat? [The answer is .807]
• March 11th 2009, 06:02 AM
mr fantastic
Quote:

Originally Posted by garrett88
Four percent of those who make an airline reservation do not show up for their flight. An airline sells 75 seats for a plane that has 73 seats (overbooking). What is the probability that every person who shows up will get a seat? [The answer is .807]

Let X be the random variable number of people who don't show up.

X ~ Binomial(n = 75, p = 0.04)

Calculate $\Pr(X \geq 2) = 1 - \Pr(X \leq 1)$.

Alternatively:

Let Y be the random variable number of people who show up.

Y ~ Binomial(n = 75, p = 0.96)

Calculate $\Pr(Y \leq 73) = 1 - \Pr(Y \geq 74)$.