Probability of overbooking seats.

An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. If the airline sells 110 tickets for a flight that has only 105 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly?

Is this a possion distribution question? I'm having hard time how to start it...

Re: Probability of overbooking seats.

It could be Poisson, I suppose, but with numbers this large, a Normal Approximation might be sufficient. On the other hand, we have only finite numbers of things, so Poisson is not suggested. Still, it might be close enough for some purposes. Think about the definitions of the distributions. Binomial is nicely finite.

Re: Probability of overbooking seats.

Quote:

Originally Posted by

**wopashui** An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. If the airline sells 110 tickets for a flight that has only 105 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly?

Is this a possion distribution question? I'm having hard time how to start it...

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

X ~ Binomial(p = 0.05, n = 110)

Calculate $\displaystyle \Pr(X \geq 5)$.

Re: Probability of overbooking seats.

Quote:

Originally Posted by

**mr fantastic** Let X be the random variable "number of people that don't show up".

X ~ Binomial(p = 0.05, n = 110)

Calculate $\displaystyle \Pr(X \geq 5)$.

sorry, can you explain why is binomial, the question is not asking the prob of how many people won't show up

Re: Probability of overbooking seats.

110 tickets

105 seats

5 ticket holders have to fail to show inorder for everyone to have a seat.

Re: Probability of overbooking seats.

Quote:

Originally Posted by

**TKHunny** 110 tickets

105 seats

5 ticket holders have to fail to show inorder for everyone to have a seat.

but everyone includes those 5 people who has reservation, isn't it asking the prob that the 5 people will have seat?

Re: Probability of overbooking seats.

Please read the problem statement carefully.

"what is the probability that a seat will be available for every person__ holding a reservation and planning to fly__?"

Those who fail to show do hold a reservation, but are not planning to fly.