There are passengers waiting in a queue to board a plane with 100 assigned seats
MATHEMATICS · Subjective · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
There are n=100 passengers waiting in a queue to board a plane with 100 assigned seats. Each passenger holds a ticket for a specific seat, numbered 1 to 100, corresponding to their position in the queue.
- The first passenger (Passenger 1) enters the plane and, having lost their boarding pass, chooses a seat uniformly at random from all 100 seats.
- Every subsequent passenger (2,3... 10) enters one by one and follows these rules:
1. If their assigned seat is empty, they must sit in it.
2. If their assigned seat is already occupied, they choose a seat uniformly at random from the remaining empty seats.
Calculate the exact probability that the last passenger (Passenger 100) ends up sitting in their own assigned seat (Seat 100).