#!/usr/bin/env python
# coding: utf-8

# In[1]:


import numpy as np
from itertools import chain


# In[2]:


get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt


# In[3]:


res = []
for _ in xrange(50000):
    kids = np.random.randint(1,10,100)

    boys = np.array([np.random.randint(0, 2, k).sum() for k in kids])
    girls = kids-boys
    
    boy_brothers = [[b-1]*b for b in boys]
    girl_brothers = [[b]*g for b, g in zip(boys, girls)]
    
    res.append(np.array(list(chain(*girl_brothers))).mean() - np.array(list(chain(*boy_brothers))).mean())
print np.array(res).mean()


# In[4]:


plt.hist(res, bins=100)
plt.show()