All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
A crazy passenger (Posted on 2002-04-18) Difficulty: 5 of 5
A line of 100 airline passengers is waiting to board the plain. They each hold a ticket to one of the 100 seats on that flight. (For convenience, let's say that the Nth passenger in line has a ticket for the seat number N.)

Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random.

What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?

See The Solution Submitted by levik    
Rating: 4.4667 (15 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution And Another | Comment 11 of 14 |
After a discussion with the wife, we came upon a slicker approach:

1) Each time a passenger does a random choice, the first and last seats are equally likely to be picked.
2) Once the first or last chair is picked, there are no more random choices.
3) The first or last chair must be picked before the last passenger comes aboard.

Thus, the last passenger has a 50% chance of being in the last chair and a 50% chance of being in the first chair.
Note the lack of dependency upon the number of passengers, and that there is a 50% chance of the last passenger not getting their chair if the first and last chair are different (n>1).

  Posted by owl on 2005-08-18 02:33:43
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information