A small regional carrier accepted 22 reservations for a...

A small regional carrier accepted 22 reservations for a particular flight with 19 seats. 13 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 59% 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 For this question, we are told that on a certain flight, there are 19 seats available, and the airline made 22 reservations for these 19 seats.

00:11 We're also told that 13 of these reservations are for regular customers who are assumed to show up.

00:18 That means, of the remaining, there are nine other reservations that are not regular customers.

00:25 And we are told for that these people, their probabilities of showing up are 59%.

00:33 And so we're asked two questions.

00:34 The probability that an overbooking occurs and the probability that the flight has empty seats.

00:40 So let's first define a random variable x as the number of the nine non -regular customers who show up for the flight.

00:48 And here each of these nine can be thought of as bernoulli trials, either shows up or not.

00:54 And if we can assume that their outcomes are independent, then the number of successes in a fixed number of independent bernoulli trials is a binomial random variable.

01:04 So x is a binomial based on nine trials and probability of success .59.

01:12 So we already know that 13 are showing up.

01:14 We will have an overbooking if a total of 20 or more show up.

01:21 So that means a total of seven or more of the nine non -regular customers.

01:28 So that is we want to find the probability that x is at least seven.

01:36 This can be expressed as one minus the probability that x is at most to 6.

01:41 And we can use excel to solve this...