https://math.stackexchange.com/q/2484696/86776

urn.rb

def run
  urn = [:blue, :blue, :red, :red, :red]
  blue = 0
  n = urn.size
  (1..n).each do |k|
    index = rand(urn.size)
    ball = urn.delete_at(index)
    #puts "ball=#{ball} urn=#{urn}"
    if ball == :blue
      blue += 1
    end
    if blue == 2
      if k % 2 == 1
        return :alice
      else
        return :david
      end
    end
  end
  throw :error
end

def experiment(n)
  alice = 0
  n.times do |i|
    winner = run()
    #puts "#{i}: #{winner}"
    if winner == :alice
      alice += 1
    end
  end
  p = alice / (1.0 * n)
  puts "n=#{n} alice wins=#{alice} => p=#{p}"
end

experiment(1_000_000)