A small regional carrier accepted 18 reservations for a...

A small regional carrier accepted 18 reservations for a particular flight with 17 seats. 11 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 43% chance, independently of each other. (Report answers accurate to 4 decimal places.) Find the probability that overbooking occurs. Find the probability that the flight has empty seats.

Transcript

00:01 We have here a binomial distribution problem.

00:06 So big x equals little x is equal to nx combinations.

00:13 That in itself is the following formula.

00:20 We have nx is equal to n factorial over x factorial times n minus x factorial.

00:37 We'll have that combination formula times our rate of success to the x power times our rate of failure, which is equal to 1 minus p, little p, to the n minus x power.

00:56 We are given a rate of success, which is 0 .43, so that gives us a rate of failure of 0 .5 .3.

01:09 7.

01:11 However, what we don't have, well, we kind of have it, but we have to adjust it, is a sample size to test for.

01:21 This is because, yes, we are told that there are 18 reservations for the flight, but we are also told that 11 of those are for people that will arrive 100 % guaranteed.

01:39 So we don't really have to find out the probability of those people arriving since they're guaranteed, right? so we'll take that 18 minus 11, which will give us a sample size of 7.

01:51 These are the amounts of people who may or may not arrive to the plane.

02:00 Now, we also have that there are 17 seats of those 17, 11 of those 17, 11 of those 17, 11 of them are going to be taken by the people who are guaranteed to arrive.

02:12 So what we actually have is six available seats.

02:20 This is important because our questions are the probability that the flight will be overbucked.

02:27 So this is that all seven of the remaining people arrive...

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