sportloto2020.py

from math import comb

def chance(k, n, K, N):
    return comb(K, k) * comb(N - K, n - k) / comb(N, n)


def fits_in_delta_prob(lower, upper, n, K, N):
    result = 0
    for x in range(n + 1):
        ratio = x / n
        if lower <= ratio <= upper:
            result += chance(x, n, K, N)
    return result


def probabilities(N, delta):
    x15 = 0.071
    x20 = 0.433
    return list(map(lambda K: (K, round(fits_in_delta_prob(x15 - delta, x15 + delta, 15, K, N) * fits_in_delta_prob(x20 - delta, x20 + delta, 20, K, N) * 100, 2)), range(N)))


def solve(N, delta):
    answer = probabilities(N, delta)
    m = answer[0]
    for a in answer:
        if a[1] > m[1]:
            m = a
    return m

solve(10000, 0.07)