Math Problem Statement

Suppose that the probability that a passenger will miss a flight is

0.09950.0995.

Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of

5353

passengers.

​(a) If

5555

tickets are​ sold, what is the probability that

5454

or

5555

passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that

5959

tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with seating capacity of

240240

​passengers, what is the largest number of tickets that can be sold to keep the probability of a passenger being​ "bumped" below

11​%?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Cumulative Probability

Formulas

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Cumulative Probability: P(X <= k) = Sum of P(X = i) for i = 0 to k

Theorems

Binomial Theorem
Probability Distribution Theorem

Suitable Grade Level

Undergraduate