What is the probability that two random lines drawn inside a square will intersect?

squares.py

import random

#Orientation and doIntersect mostly copied wholesale from here:
# http://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
# with some modifications because I can safely ignore their special cases.

def orientation(p, q, r):
	val = (q[1] - p[1]) * (r[0] - q[0]) - (q[0] - p[0]) * (r[1] - q[1])
	if val == 0:
		return val #colinear

	retval =  1 if (val > 0) else 2
	return retval

def doIntersect(p1, p2, q1, q2):
	o1 = orientation(p1, q1, p2)
	o2 = orientation(p1, q1, q2)
	o3 = orientation(p2, q2, p1)
	o4 = orientation(p2, q2, q1)

	if (o1 != o2 and o3 != o4):
		return True

	return False


def makeRandPoint():
	#Let's say our random square goes from 0,0 to 10,10
	#Figure out which wall the point is on
	wall = random.randint(0,3)
	if wall == 0:
		return (0,random.random() * 10)
	if wall == 1:
		return (random.random() * 10,0)
	if wall == 2:
		return (10,random.random() * 10)
	if wall == 3:
		return (random.random() * 10,10)


def main():

	intersections = 0

	for i in range(1000000) :
		p1 = makeRandPoint()
		p2 = makeRandPoint()
		q1 = makeRandPoint()
		q2 = makeRandPoint()
		if doIntersect(p1, p2, q1, q2):
			intersections = intersections + 1

	print (str(intersections) + " intersections of 1,000,000 found.")


main()