2009 passengers are waiting in a line to board an airplane with 2009 seats. The seats are numbered from 1 to 2009. Each passenger has a boarding pass that has his/her seat number on it. However, these passengers are oblivious to their boarding pass and choose their seats at random, each with a uniform probability from the available empty seats.
What is the probability that everyone's actual seat number and their assigned seat number differ by at most 1? That is, no one sits more than 1 seat away from their assigned seat.
Showing posts with label airplane. Show all posts
Showing posts with label airplane. Show all posts
Tuesday, October 27, 2009
Friday, October 16, 2009
Passengers Boarding Airplane
2009 passengers are waiting in a line to board an airplane with 2009 seats. Each passenger has a boarding pass that has his/her seat number on it. The first passenger, however, was oblivious and chose a random seat to sit on.
For each subsequent passenger, he/she will try to sit on his/her assigned seat first. If that seat is taken by someone else, he/she will choose a random empty seat to sit on.
What is the probability that the last passenger would sit on his assigned seat?
Solution: http://dharmath.blogspot.com/2010/05/solution-passengers-boarding-airplane.html
For each subsequent passenger, he/she will try to sit on his/her assigned seat first. If that seat is taken by someone else, he/she will choose a random empty seat to sit on.
What is the probability that the last passenger would sit on his assigned seat?
Solution: http://dharmath.blogspot.com/2010/05/solution-passengers-boarding-airplane.html
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