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?
Best Answer
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.