from fractions import Fraction
from math import prod
def probabilities(x, y, z):
    r1,r2 = Fraction(x[0], sum(x)),Fraction(y[0], sum(y))
    b1,b2 = Fraction(x[1], sum(x)),Fraction(y[1], sum(y))
    r3,b3 = Fraction(z[0], sum(z)),Fraction(z[1], sum(z))
    return [(r1,r2,b3),(r1,b2,r3),(b1,r2,r3)]

def calc_prob(x, y, z):
    to_mult = probabilities(x, y, z)
    prob = Fraction(0,1)
    for m in to_mult:prob += prod(m)
    return prob

x,y,z= (4, 3),(5, 4),(4, 4)

probability = calc_prob(x, y, z)
print(f"{probability.numerator}/{probability.denominator}")