The Airplane Seating Problem

The problem
P1 🍷P100?100 seats · passenger 1 picks at randomdoes P100 get seat 100?

100 passengers board a plane with 100 numbered seats. Each has a ticket for a specific seat. Passenger 1 is drunk, forgets his ticket, and picks a seat at random. Every subsequent passenger:

  • Sits in their assigned seat if it's free.
  • Otherwise, picks a random empty seat.

What's the probability that passenger 100 ends up in seat 100?