Discrete mathematics: Simulate the probability question

Question

Problem

There are 1, 2, 3, 4 number card in a bag.

• If you pick up 1, add one white ball into box_b.
• If you pick up 2 or 3, add one white ball and one balck ball into box_b.
• If you pick up 4, add two white balls and one black ball into box_b.
• You must put the card back in your pocket every time you pull it out.
• You have to do this 4 times.

When there are 8 balls in box_b, what is the probability that the number of black balls in the box is 2?

Code

import math

#흰공=0 검은공=1
box_b = list()

#조건부확률 = box_b 원소 개수 8개(=e)이면서 1이 2개(=f)일 확률 / e 확률
cnt_e = 0 
cnt_ef = 0

for i in range(1, 5) : 
    if i == 1 :
        box_b.append(0)
    if i == 2 or i == 3 :
        box_b.append([0, 1])
    if i == 4 :
        box_b.append([0, 0, 1])
    for j in range(1, 5) :
        if j == 1 :
            box_b.append(0)
        if j == 2 or j == 3 :
            box_b.append([0, 1])
        if j == 4 :
            box_b.append([0, 0, 1])
        for k in range(1, 5) :
            if k == 1 :
                box_b.append(0)
            if k == 2 or k == 3 :
                box_b.append([0, 1])
            if k == 4 :
                box_b.append([0, 0, 1])
            for l in range(1, 5) :
                if l == 1 :
                    box_b.append(0)
                if l == 2 or l == 3 :
                    box_b.append([0, 1])
                if l == 4 :
                    box_b.append([0, 0, 1])
                print(box_b)

output

Output should be like [0, [0,1], [0,0,1], [0,1]], [...], but it's output is [0, [0,1], 0, [0,1], 0, [0,1], 0, [0,1] .... (very long list)...] [..]

What's wrong with my code?

• My teacher said that the box_b should be reseted when i, j, k, l change. Because of it, the result has been piled up. But he and I don't know which line the reset point should go into.

++ It is not duplicate : I tried i == 2 or i == 3(seperation of two conditions), but it isn't major problem which I look for. There are still problems.

Answer 1

This is how simulating the problem would look like:

import random

random.seed(1)


def calc_prob(bag, sims):
    def pick():
        card = None
        while card is None:
            card = random.choice(bag)
            if card is not None:
                bag[card] = None
                break
        return card

    eights = 0
    blacks = 0
    for _ in range(sims):
        box_b = []
        for _ in range(4):
            card = pick()
            if card == 1:
                box_b.append(0)
            elif card == 2 or card == 3:
                box_b.extend([0, 1])
            elif card == 4:
                box_b.extend([0, 0, 1])

        if len(box_b) == 8:
            eights += 1
            if box_b.count(1) == 2:
                blacks += 1

    return blacks / eights if eights else 0


sims = 100000
bag = [1, 2, 3, 4] * (sims + 1)
print(calc_prob(bag, sims))

Prints

0.08484606447865234

Note:

• Every time you pick a card, the card should be removed from the bag and that card is no longer in the "pool" of cards.