Probability Question (Not About Sports)

[daneault23]

Suppose a plane has 200 seats and 225 tickets are sold for that flight. 8% of the people of bought tickets don't show up. What's the probability that the airline will be able to accommodate all of the ticketed passengers that show up?

Seems like answer should be 0? There are 207 passengers who show up and only 200 seats for them... What am I missing?

[flocko76]

it depends on what you mean by accommodate. I know of people who love that situation. the get free tickets from the airline to get bumped to a later flight. plus hotel accommodations.

[daneault23]

By "accommodate" they mean are able to get a seat on the flight.

[cyberbabble]

You should say that over a series of flights an average of 8% don't show up. Sometimes more, sometimes less. What is the probably that on a given flight 25 or more will not show up.

Don't know stats well enough to answer it.

[cyrusii]

Generally, in these type of questions they mean that the probability of each person not showing up is 8%. Not that exactly 8% won't show up.

It is a basic Bernoulli question (google Bernoulli distribution, if you are not familiar).
Probability of success: 0.08
Number of trials: 225
What you want: probability of number of success being higher or equal to 25 (meaning at least 25 people won't show up)

Put it into a Bernoulli calculator, doing it with pen an paper is super tedious. It is about 6%.

[Blax0r]

Generally, in these type of questions they mean that the probability of each person not showing up is 8%. Not that exactly 8% won't show up.

It is a basic Bernoulli question (google Bernoulli distribution, if you are not familiar).
Probability of success: 0.08
Number of trials: 225
What you want: probability of number of success being higher or equal to 25 (meaning at least 25 people won't show up)

Put it into a Bernoulli calculator, doing it with pen an paper is super tedious. It is about 6%.

This is the right way to solve the problem, assuming that the "8% of people not showing up" really means each person has an 8% probability of not showing up.