# Crazy guy on Aeroplane Puzzle

Crazy Guy on Aeroplane Puzzle

A line of 100 airline passengers is waiting to board a plane. 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 of 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) ?

There could be a whole lot of possibilities and one of them is:

1) The probability that none of the people are sitting in their respective seats except the last one which can be given by

1-(1-1+1/2!-1/3!…..+(-1)^n/99!)

1/2 is the answer

can anyone PLEASE just post the answer