100 Seats

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace SeatProblem
{
    class Program
    {
        //entry point
        public static void Main()
        {
            Random rng = new Random(); //Create a RNG
            const int n = 10000000; //number of trials
            int lastSeatAvailableCounter = 0; //counter that we will increase each time the last seat is available

            //loop N times
            for (int trials = 0; trials < n; trials++)
            {
                int[] seats = new int[100]; //array of 100 seats

                //fill the seats array with 0
                for (int i = 0; i < 100; i++)
                    seats[i] = 0;

                //pick a random seat for first person
                int firstSeat = rng.Next(0,100);
                seats[firstSeat] = 1;

                //loop to seat people 2-100
                int currentPerson = 2;
                while (currentPerson <= 99)
                {
                    int seatNumber = currentPerson - 1;

                    while (seats[seatNumber] != 0)
                        seatNumber = rng.Next(0,100); //pick a random number from 0-100 (not inclusive of 100)

                    seats[seatNumber] = currentPerson;
                    currentPerson++;
                }

                //if last seat is available, increment counter by 1
                if (seats[99] == 0)
                    lastSeatAvailableCounter++;
            }

            double result = (double)lastSeatAvailableCounter / (double)n;
            Console.WriteLine(lastSeatAvailableCounter);
            Console.WriteLine(result);
            Console.ReadKey();

        }
    }
}