The Lost Boarding Pass
One hundred passengers line up to board an airplane, but the first has lost his boarding pass and takes a random seat instead. Each subsequent passenger take his or her assigned seat if available, otherwise a random unoccupied seat.
What is the probability that the last passenger to board finds his seat occupied?
What is the probability that the last passenger to board finds his seat occupied?
posted by Zaux at
8:43 PM
6 Comments:
1 to 100..
Without doing any number crunching I'd say ~49-50%.
Rationale:
-1/100 chance of 1st passenger finding his right seat=1%
-following that, any collision will result in a random selected seat, in which, the last guys seats is as equally likely as the 1st passengers correct seat to be chosen.~=50%
100%-(50+1)%=49%
Reason the answer will be more than 49%:
-once the last passengers seat has been selected it can't be unselected
-when the random selected passenger seat is filled, subsequent collisions from previous randoms may result in them filling the last passengers seat. I would suspect this translates to something on the order of 1%.
so somewhere between 49-50%
Cam
Zaux, please don't post the solution yet. I will have a bash later, but I've got to work now.
By considering 2, 3 and 4 seats (rather than 100), I keep getting 50%. So I expect that the probability is 1/2 regardless of the number of seats (as long as all the seats are fuly booked).
OK, I'm done.
50% is the correct answer
I definitely bow to Cam's instinct. I was quite surprised at the answer.
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