A line of 100 airline passengers is waiting to board a plane.

gistfile1.rb

=begin
  A line of 100 airline passengers is waiting to board a plane. 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 of
  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)?  
=end

def place_passenger(n)
  if @seats[n] == :free
    @seats[n] = :taken
  else
    new_seat = rand (1..Max_seat)
    until (@seats[new_seat] == :free) 
      new_seat = rand (1..Max_seat)
    end
    @seats[new_seat] = :taken
  end
end

Samples = 53280
Max_seat = 100
@seats = Array.new(Max_seat+1) {:free}
got_seat = 0

1.upto(Samples) do |i|
  crazy_seat = rand (1..Max_seat)
  @seats[crazy_seat] = :taken
  2.upto(Max_seat-1) {|n| place_passenger(n) }
  got_seat += 1 if @seats[Max_seat] == :free
  @seats.fill(:free)
end

puts "The chance of getting the seat is about #{got_seat/Samples.to_f}"