solution

from random import randint

"""Create four random points:
A in upper left quadrant
B in lower left quadrant
C in lower right quadrant
D in upper right quandrant
Calculate slopes
Return False if non-convexness detected"""

def run_once():
    ax = float(randint(1,99999)) #Random x-value for A 
    ay = float(randint(1,99999) + 100000) #Random y-value, pushed to upper half
    bx = float(randint(1,99999))
    by = float(randint(1,99999))
    cx = float(randint(1,99999) + 100000)
    cy = float(randint(1,99999))
    dx = float(randint(1,99999) + 100000)
    dy = float(randint(1,99999) + 100000)
    if ax == bx: #Making sure we don't divide by zero
        abslope = 999999.0
    else:
        abslope = (ay - by) / (ax - bx)
    adslope = (dy - ay) / (dx - ax)
    if cx == dx:
        cdslope = 999999.0
    else:
        cdslope = (dy - cy) / (dx - cx)
    bcslope = (by - cy) / (bx - cx)
    if abslope > 0 and adslope > abslope: #Check corner in A quadrant
        return False
    elif cdslope < 0 and adslope < cdslope:
        return False
    elif cdslope > 0 and bcslope > cdslope:
        return False
    elif abslope < 0 and bcslope < abslope:
        return False
    else:
        return True

def run_a_lot(times):
    count = 0
    for i in range(times):
        if run_once():
            count += 1.0
    return count / times

print run_a_lot(1000000)
print run_a_lot(1000000)
print run_a_lot(1000000)