#!/usr/bin/perl

use strict;

my $numtrials = 1000000;

# tweak these probabilities experimentally to see outcomes
my $background_probability_1 = 0.81;
print "Background probability 1: $background_probability_1\n";
my $background_probability_2 = 0.61;
print "Background probability 2: $background_probability_2\n";

# Sample sizes and observed rates; leave these fixed
my $sample_size_1 = 47;
my $sample_size_1_threshold = 36; # we count the times our sample goes *below* this threshold
my $sample_size_2 = 54;
my $sample_size_2_threshold = 38; # we count the times our sample goes *above* this threshold

my $times_threshold_1_met = 0;
my $times_threshold_2_met = 0;
my $times_both_thresholds_met = 0;
for (my $i = 1; $i <= $numtrials; ++$i)
{
	my $threshold_1_met = 0;
	my $threshold_2_met = 0;

	my $count_1 = 0;
	for (my $j = 0; $j <= $sample_size_1; ++$j)
	{
		if (rand(1) < $background_probability_1)
		{
			++$count_1;
		}
	}
	if ($count_1 <= $sample_size_1_threshold)
	{
		$threshold_1_met=1;
	}

	my $count_2 = 0;
	for (my $j = 0; $j <= $sample_size_2; ++$j)
	{
		if (rand(1) < $background_probability_2)
		{
			++$count_2;
		}
	}
	if ($count_2 >= $sample_size_2_threshold)
	{
		$threshold_2_met=1;
	}

	if ($threshold_1_met) { ++$times_threshold_1_met; }
	if ($threshold_2_met) { ++$times_threshold_2_met; }
	if ($threshold_1_met && $threshold_2_met) { ++$times_both_thresholds_met; }
}

print "Times threshold 1 met: $times_threshold_1_met/$numtrials\n";
print "Times threshold 2 met: $times_threshold_2_met/$numtrials\n";
print "Times both thresholds met: $times_both_thresholds_met/$numtrials\n";