An airline knows that 5 percent of the people making...

Name: An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up?
Uploaded: 2022-01-15T14:47:47-08:00
Duration: 6 min 38 s
Channel: Brent Burkett
Description: An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up?

An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up?

Transcript

00:01 Okay, so in this problem, there's an airline.

00:03 They know that 5 % of people won't show up for their flight.

00:07 So what they do is they sell 52 tickets for a flight that only has 50 seats.

00:12 So they're overselling their seats.

00:14 And we want to know what is the probability that all passengers who show up get a seat.

00:20 All right.

00:22 So here's the thing you got to remember.

00:24 So the probability of a person showing up shows, right, is not.

00:31 95 % or 0 .95 that they show up.

00:36 Person not showing up, the probability of absent is 0 .05, 5%.

00:46 Okay? so, instead of trying to figure out, well, what's the probability that exactly 50 people show up or less, the best thing to do is you do with the complement.

00:57 You say, well, what's the probability of all 52 showing up? figure out what that is what's the probability of just exactly 51 people showing up and then add those two subtract it from 100 percent and that's going to be the probability that everybody gets a seat okay so the probability that all 52 show up everybody shows up is right the probability someone shows up is 0 .95 and there's 52 of them so that's really raised to the 52 power, 52 power.

01:36 So all that comes out to be, it's a really dinky number.

01:40 So that's about 0 .069.

01:45 Type that into your calculator.

01:47 Good.

01:47 All right.

01:48 Now, the probability that exactly 51 show up, this one gets a little tricky.

01:55 Exactly 51.

01:59 So what that's going to be, we have to use this formula.

02:03 So how many different ways can we have.

02:07 51 people show up.

02:10 So there's a little formula.

02:12 Okay.

02:12 And the order doesn't matter when they should.

02:14 So it's 51.

02:20 That's not right.

02:22 52 because there's 52 possible, but we're only choosing 51.

02:28 It's actually combinations of 51.

02:31 So if you have 52 objects, how many ways can you combine them in groups of 51? okay.

02:40 So that's a probability, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, that's, uh, so.

02:43 Uh, okay...

Question

An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up?

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