LOL @ this brain teaser I got on a quantitative finance website:

[Lucky Luciano]

It is actually a good question, but you will have no chance unless you are mathematically inclined. Either way, it is a funny question:

100 people are in line to board Airforce One. There are exactly 100 seats on the plane.

Each passenger has a ticket. Each ticket assigns the passenger to a specific seat. The line of passengers boards Airforce 1, one at a time.

GW is the first to board the plane. He cannot read, and does not know which seat is his.

In order to cover up his inability, he picks a seat at random and pretends that it is his proper seat.

The remaining passengers board the plane one at a time. They all know that GW cannot read, but none of them has the guts to point it out, so they play along with GW.

If one of them finds their seat empty, they will sit. If they find that their seat is already taken, they will pick a seat at random.

This continues until everyone has boarded the plane and taken a seat.

What is the probability that the last person to board the plane sits in their proper seat?

What is the expected number of people sitting in their proper seats?
********************

The solution is at:

http://www.wilmott.com/messageview.cfm?catid=26&threadid=23067

[Droopy]

1. I actually recognized some of the math

from the statistics course I took in college. But I would have never been able to solve this problem.

[Thor_MN]

2. 100% because Dumbass is on a flight to Tibet. He can't read.

And he can't do anything without screwing up.

[Lucky Luciano]

3. HAHA - I should have thought of that! nt

[Guaranteed]

4. Well, this is hard...trying to figure it out...

As to the first question, we'll call "n" the running tally of people who have run into someone else in their seat and subsequently had to sit in someone else's seat. n is going to have to be greater than or equal to 1, because Chimpy is in someone's seat already, and that person is going to have to sit in someone else's- there's an off chance that would be Chimpy's seat, though, in which case the final n would be 1.

The thing is, though, until that happens- that is, until someone else sits in Chimpy's seat after having their seat already taken- n will continually keep turning into n + 1, automatically, because someone else is always going to have their seat taken by that person who had their seat taken when they sit down. So n will continue to increase until Chimpy's seat is filled.

This chain reaction has to stop in order for the last person to sit in their own seat, or someone else will have sat in it before they get to it. Also, the last empty seat on the plane can not be a seat other than Chimpy's or the last passenger's- otherwise, the passenger who was supposed to sit in that seat would have SAT in that seat. Therefore, the chance of the last person having their seat available is the chance that someone will sit in Chimpy's seat before he finally boards the plane.

What the hell that is- I honestly can't tell you. I'd have to guess either 99/100 or 50/100.

[Lucky Luciano]

5. There is a solution posted from my link

The probability of the last person getting the right seat is indeed 50%. The expected number of people in the right seat is a much harder question and it is approximate 94.8.

Check the solution.