Help needed

Hi, not sure how to resolve the following:

An airplane as a capacity of 23 passengers. The airline knowning that 10% of passengers who have reserved a seat do not show up at boarding. Thus the airline always accept more reservation then available place.

1- What is the probability that all passenger that show up for boarding can get a seat if the company as accepted 25 reservation.

2- If we have 3 flight per day, what is the probability that for each flight all passengers that show up can have a seat. We suppose that 25 reservations were made for each flight.

Tks for the help.


TS Contributor
The probability of any given passenger showing up for a flight is 90%, so you need to find the probability of 23 or fewer people showing up for a flight.

1 - Use the binomial probability distribution (with p=.9, q = 1-p = 0.1) and find the probability of 25 people and 24 people showing up. Add these probabilities, then subtract the sum from 1. That will give you the probability of everyone getting a seat.

2 - Take the answer from #1 above and raise it to the 3rd power (^3).