python中的概率计算

Question

My problem is: I have 12 players, with 3 of them being named A, B and C, respectively. 12 players are being divided into 2 groups, 6 people each. I need to calculate the probability of player A and B being in the same team, and player C being in thе eopposite one. Math is not my strongsuit, because im pretty sure this is not a hard thing to calculate, but i would be really grateful if you could help me with this one. Here is what i wrote so far:

import random

playersnumb = 12
players = list(range(12))

A = random.choice([x for x in range(12)])

B = random.choice([x for x in range(12) if x != A])

C = random.choice([x for x in range(12) if (x != A) and (x != B)])

random.shuffle(players)
team1 = (players[:6])
team2 = (players[6:])

if A in team1:
    print("Player A is in team 1")
else:
    print("Player A is in team 2")
if B in team1:
    print("Player B is in team 1")
else:
    print("Player B is in team 2")
if C in team1:
    print("Player C is in team 1")
else:
    print("Player C is in team 2")

Any help is appreciated.

Answer 1

The number of ways to fill 1 list of six total = 12!/(6! * 6!) comb(12,6)

The number of ways to fill a list of six (including A and B and not C) = 9!/(4! * 5!) comb(9, 4)

Also, want to find (not A and not B and C) = 9!/(5! * 4!) comb(9, 5)

>>> from math import comb
>>> comb(12, 6)
924
>>> comb(9, 4) + comb(9, 5)
252
>>> 252 / 924
0.2727272727272727

Answer 2

I wrote a little bit based on your code. The idea is to loop multiple times over your test code, it is not 100% accurate, but i think good enough for you:

import random


def calculate(playercount: int = 12) -> bool:
    players = list(range(playercount))

    player_a = random.choice([x for x in range(playercount)])

    player_b = random.choice([x for x in range(playercount) if x != player_a])

    player_c = random.choice([x for x in range(playercount) if (x != player_a) and (x != player_b)])

    random.shuffle(players)
    team1 = (players[:playercount//2])
    team2 = (players[playercount//2:])

    # That are your "positive" events
    return (player_a in team1 and player_b in team1 and player_c in team2) or\
           (player_a in team2 and player_b in team2 and player_c in team1)


def calculate_all(runtimes: int = 100000) -> float:
    counter = 0
    # count all poyitive events
    for i in range(runtimes):
        if calculate():
            counter += 1

    # return how often they appeared, based on all tests
    return counter / runtimes


print("The probability is about {} %".format(calculate_all() * 100))