# What is the probability that the flight departs with empty seats?

Because not all airline passengers show up for their reserved seats, an airline sells 125 tickets for a flight that holds 120 passengers. The probability that a passenger does not show up is 0.10, and passengers behave independently.

What is the probability that the flight departs with empty seats?

• What do you need to know to start with? Feb 1, 2017 at 3:07

The number of passengers showing up is a random variable $X\sim\text{Binomial}(125,0.9)$

And what you want is

$$P(X\le 119)=F_X(119)=\\=1-P(X=125)-P(X=124)-P(X=123)-P(X=122)-P(X=121)-P(X=120)$$

You may calculate it numerically with a computer program, or do a normal approximation.

• And it is marginally easier to calculate : $1-P(120\leq X\leq 125)$ Feb 1, 2017 at 3:10