https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)

random_chord_1.php

<?php

function random() {
	return mt_rand() / mt_getrandmax() * 2 - 1;	
}
$a = sqrt(3);
//$a = 1/2.0;
$n = 10000000;
$c = 0;
$Xsum = 0;
for ($i = 0; $i < $n; $i++) {
	$x1 = random();
	$x2 = random();
	$Xsum += $x1;
	
	$y1 = sqrt(1 - $x1*$x1);
	if (random() >= 0) {
		$y1 = -$y1;
	}
	
	$y2 = sqrt(1 - $x2*$x2);
	if (random() >= 0) {
		$y2 = -$y2;
	}
	
	$l = sqrt(($y1 - $y2)*($y1 - $y2) + ($x2 - $x1)*($x2 - $x1));
	
	if ($l >= $a) $c++;
}
echo $c/$n;
echo '<br>';
echo $Xsum/$n;

random_chord_2.php

<?php

function random() {
	return mt_rand() / mt_getrandmax() * 2 - 1;	
}
function random_angle() {
	return mt_rand() / mt_getrandmax() * 360;	
}
$a = sqrt(3);
//$a = 1/2.0;
$n = 100000;
$c = 0;
$Xsum = 0;
for ($i = 0; $i < $n; $i++) {
	$a1 = random_angle();
	$a2 = random_angle();
	$x1 = sin(deg2rad($a1));
	$x2 = sin(deg2rad($a2));
	$Xsum += $x1;
	$y1 = cos(deg2rad($a1));
	$y2 = cos(deg2rad($a2));
	
	$l = sqrt(($y1 - $y2)*($y1 - $y2) + ($x2 - $x1)*($x2 - $x1));
	
	if ($l >= $a) $c++;
}
echo $c/$n;
echo '<br>';
echo $Xsum/$n;