Magnet

The percentage of landing on the first quadrant is $70\%$ , and $10\%$ for all second, third and forth quarter.

Using the probability distribution above your code might looks complicated. Instead, it can be transformed as :

The percentage of landing on the first quadrant is $60\%$ , and $40\%$ will evenly land on any point on the board.

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import math
from random import randint

def dist(x1,y1,x2,y2):
    return math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2))

tst = 0
ans = 0
while True:

    # first point
    case = randint(1,10)     # 1 <= case <= 10
    if case <= 6:            # first quadrant
        x1 = randint(0,100) / 100.0
        y1 = randint(0,100) / 100.0
    else:                    # full board
        x1 = randint(0,200) / 100.0
        y1 = randint(0,200) / 100.0

    # second point
    case = randint(1,10)
    if case <= 6:
        x2 = randint(0,100) / 100.0
        y2 = randint(0,100) / 100.0
    else:
        x2 = randint(0,200) / 100.0
        y2 = randint(0,200) / 100.0

    d = dist(x1,y1,x2,y2)

    tst += 1
    ans += d

    print tst, ans / tst

Relevant wiki: Monte-Carlo Simulation

Python 3.5.1:

import random
from math import sqrt

def generatepoint():
    seed = random.randint(1,100)
    quadrant = None
    if 1<=seed<=70:
        quadrant = 1
    elif 71<=seed<=80:
        quadrant = 2
    elif 81<=seed<90:
        quadrant = 3
    else:
        quadrant = 4

    x=random.randint(0,100)
    y=random.randint(0,100)
    if quadrant==1:
        pass
    elif quadrant==2:
        y=-y
    elif quadrant==3:
        x=-x
        y=-y
    else:
        x=-x
    return (x,y)

def distance(point1,point2):
    return sqrt((point1[0]-point2[0])**2+(point1[1]-point2[1])**2)

ave = 0
for i in range(0,100000):
    a=generatepoint()
    b=generatepoint()
    ave+=distance(a,b)
print (ave/100000)