# Probability of overbooking seats.

• Jul 5th 2011, 08:06 PM
wopashui
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...
• Jul 5th 2011, 08:20 PM
TKHunny
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.
• Jul 5th 2011, 08:21 PM
mr fantastic
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 $\Pr(X \geq 5)$.
• Jul 6th 2011, 06:15 PM
wopashui
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 $\Pr(X \geq 5)$.

sorry, can you explain why is binomial, the question is not asking the prob of how many people won't show up
• Jul 6th 2011, 07:21 PM
TKHunny
Re: Probability of overbooking seats.
110 tickets
105 seats
5 ticket holders have to fail to show inorder for everyone to have a seat.
• Jul 6th 2011, 07:34 PM
wopashui
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?
• Jul 6th 2011, 07:36 PM
TKHunny
Re: Probability of overbooking seats.