One hundred people line up to board an airplane. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats at random otherwise. What is the probability that the last person to board gets to sit in his assigned seat?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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One hundred people line up to board an airplane. Each has a boarding pass with assigned
seat. However, the first person to board has lost his boarding pass and takes a random seat.
After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats
at random otherwise. What is the probability that the last person to board gets to sit in his
assigned seat?

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