A line of 100 airline passengers is waiting to board the plain. 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 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)?
(In reply to
re: re Solution by levik)
axiom:
passenger n seat not taken seat 1 or another > n taken
let n = 99
if seat 99 is not taken, then seat 1 or 100 taken. there is equal
chance that someone sat in 1 or 100, 1/2
(passenger 99 will sit in 99)
if seat 99 is taken, then seat 1 and 100 are free. passenger
99 has 1/2 chance of taking 1 and 100.
the two cases are exhaustive, and either way there is
1/2
re(2): re Solution
