Assume that 100 passengers waiting to go on board for their flight. Each passenger has his own seat. Now unfortunately the passenger number one is drunk and he is gonna take one of the 100 seats randomly. For one of the rest 99 passengers, if his seat has not been taken before he entered the plane, then he normally take his own seat; otherwise he will take a vacant seat randomly. Now the problem comes: what is the probability that the last passenger can be seated in his own seat?
I tried to calculate the probability when there are totally 2, 3, 4, 5 passengers and found that P=1/2. So I think using induction is OK to prove that P=1/2 for arbitrary n. But is there any alternative methods?
Thanks!
