Question:

An airline has a policy of booking 21 persons on an airplane that can only seat 20. Past studies show that 88% of the booked passengers actually arrive for the flight. Find the probability that if the airline books 21 persons, not enough seats will be available. Is this probability low enough so that overbooking is not a real concern for passengers?

My work:

n=21

p=.88

q=.12

21C21 (.88)^21(.12)^0

= .0683

= 7%

No, because that means that there is a 7% chance of not having enough seats. Too high, I wouldn't want to take that risk.

I feel like I am missing steps, but do not know where? Please help!