Problem 46 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 46: As in 45, but this time: what is the probability of r matches?

#!/usr/bin/env ruby

TRIALS=1000000

deck = (0..51).to_a

# We shuffle the deck, then shuffle another.
# We then walk the two arrays side-by-side, checking
# for matches

# a count of how many times we got a given number of matches
matches = deck.map { 0 }

TRIALS.times do
  upper = deck.shuffle
  lower = deck.shuffle

  match = 0

  upper.each_with_index do |u_i, i|
    l_i = lower[i]
    match += 1 if l_i == u_i
  end
  matches[match] += 1
end

puts "Out of #{TRIALS}, we got the following distribution:"
matches.each_with_index { |m_i, i| puts "\t#{i}\t#{m_i}" }

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.