xkcd 3015 - D Combinatorics

xkcd3015.py

#!/usr/bin/python
from collections import defaultdict
from fractions import Fraction
from functools import reduce
from math import comb

def lhs():
	return Fraction(comb(5, 2), comb(10, 2))

def rhs():
	dice = [d(6)] * 3 + [d(4)]
	probs = reduce(convolve, dice)
	return sum(p for n,p in probs.items() if n >= 16)

def d(n):
	return {i: Fraction(1,n) for i in range(1, n+1)}

def convolve(a, b):
	res = defaultdict(lambda: Fraction(0))
	for n1, p1 in a.items():
		for n2, p2 in b.items():
			res[n1 + n2] += p1 * p2
	return res

l = lhs()
print(f"Chance of drawing arrows: {float(l*100):.02f}% ({l})")
r = rhs()
print(f"Chance of rolling dice: {float(r*100):.02f}% ({r})")