## Problem 19 of Monte Carlo solutions to Fifty Challenging Problems...

(This is another part of the Fifty Problems series, a set of example applications of Monte Carlo methods. In each post, I present source code which answers a probabilistic question using simulated models of the underlying system.)

Problem 19: Which is most likely: a) at least 1 six when rolling 6 dice, b) at least 2 sixes in 12 dice rolled, or c) at least 3 sixes of 18 dice?

#!/usr/bin/env ruby
TRIALS=10000
n_ones = 0
n_twos = 0
n_threes = 0
def roll
return 1+rand(6)
end
TRIALS.times do
six = (1..6).to_a.map { roll() }
twelve = (1..12).to_a.map { roll() }
eighteen = (1..18).to_a.map { roll() }
n_ones += 1 if six.select { |r| r == 6 }.length >= 1
n_twos += 1 if twelve.select { |r| r == 6 }.length >= 2
n_threes += 1 if eighteen.select { |r| r == 6 }.length >= 3
end
puts "After #{TRIALS}, got #{n_ones} / #{n_twos} / #{n_threes}"

I've been coding my way through *Fifty Challenging Problems in Statistics with Solutions*. This post is a part of the *Fifty Challenging Problems* series.

*This was brought to you by Josh Myer.* He has other
fun things at his homepage.