question

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?

my 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 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 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 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 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?