Imagine people boarding a plane and the first one sits at the wrong place. Every next one sits at his own place if it is available, or at a random place if not. What is the chance that the last person boarded sits at his own place?

WrongSeatSimulation.java

import java.util.Arrays;
import java.util.Random;

public class WrongSeatSimulation {
    private static final int AVAILABLE = -1;

    static boolean simulate(Random rnd, int numberOfSeats) {
        int[] seats = new int[numberOfSeats];
        Arrays.fill(seats, AVAILABLE);

        seats[rnd.nextInt(numberOfSeats-1) + 1] = 0;
        boolean ownSeat;
        for (int i=1; i<seats.length; i++) {
            int available;
            if (seats[i]==AVAILABLE) {
                available = i;
            } else {
                do {
                    available = rnd.nextInt(numberOfSeats);
                } while (seats[available]!=AVAILABLE);
            }
            seats[available] = i;

            for (int j = 0; j < seats.length; j++) System.out.print(
                    seats[j]==j         ? "O" :
                    seats[j]==AVAILABLE ? "." : "X"
            );
            System.out.println();
        }

        return seats[numberOfSeats-1] == numberOfSeats-1;
    }


    private static double simulateMany(Random rnd, int numberOfSeats, int rounds) {
        double pct = 0;
        for (int i=1; i<rounds; i++) {
            if (simulate(rnd, numberOfSeats)) pct++;
        }
        return pct / rounds * 100;
    }

    public static void main(String[] args) {
        Random rnd = new Random();
        System.out.printf("%.2f\n", simulateMany(rnd, 100, 100));
    }
}