A combination problem. Put balls into pockets, each can hold up to 2 balls, randomly. Get the average percentage of balls that are inside full pockets.

balls_and_pockets.py

import random

class Pocket(object):
    """A pocket can hold up to 2 balls."""
    def __init__(self, num):
        self.num = num
        self.member = []
        self.limit = 2
    
    @property
    def is_full(self):
        return len(self.member) == self.limit
    
    def add_member(self, member):
        if self.is_full:
            raise Exception('Pocket is full')
        self.member.append(member)
        return self.member

def seed_balls(nballs, npockets):
    """Put balls into pockets randomly."""
    # Generate pockets.
    available_pockets = []
    full_pockets = []
    for i in range(npockets):
        available_pockets.append(Pocket(i))
    
    for i in range(nballs):
        selected = random.sample(available_pockets, 1)[0]
        selected.add_member(i)
        if selected.is_full:
            full_pockets.append(selected)
            del available_pockets[available_pockets.index(selected)]
    return len(full_pockets)
        
def ave(n, nballs, npockets):
    """Perform n independent runs to obtain average percentage of balls
    that are in full pockets.
    """
    ave_full = 0
    for i in range(n):
        ave_full += seed_balls(nballs, npockets)
    print(ave_full * 2.0 / n / nballs)