I don't have a sense of "quiz asking investment sense", so I tried to solve it with brute force (Python Monte Carlo simulation)

An interesting quiz was given in the past article of "ROKO HOUSE Siegel style logical investment technique".

[Quiz to ask investment sense ]

The problem is as follows.

In countries that only want boys, every house keeps growing children until a boy is born. When I have a girl, I will have another child. When a boy is born, he will no longer have children. What is the gender ratio in this country?

• The probability that a man and a woman will be born is 1/2 each. From the unofficial Google entrance exam

I intuitively thought, "Every house has one boy. Is there a little more girls because they keep having children until they are born?"

Click here for the answer article. I think it's a good idea to think for yourself before looking at it.

[Quiz to ask investment sense <Answer / Explanation>]

My intuition was wrong, so I actually tried to see if the answer was really correct.

We asked a million couples to make children until a boy was born.

Actually, it is impossible unless it is a dictatorship, so I did it with Python code.

Is this also a kind of Monte Carlo simulation?

Below are the results. I think it's a good idea to think for yourself before looking at it. (Hereafter spoilers)

I confirmed it with the following code.

python

import numpy as np
import pandas as pd
import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.set()

dic =  {'boys':[],
        'girls':[]}

n_couples = 1000000

for i in range(n_couples):
    n_girls = 0
    n_boys = 0
    while True:
        baby = random.choice(['boy','girl'])
        if baby=='boy':
            n_boys += 1
            break
        else:
            n_girls += 1
            
    dic['boys'].append(n_boys)
    dic['girls'].append(n_girls)

df = pd.DataFrame(dic)
df.index.name = 'parent_id'
df['total'] = df.sum(axis = 1)

print("Born from a million couples,")
print("Number of boys:{:>7}".format(df['boys'].sum()))
print("Number of girls:{:>7}".format(df['girls'].sum()))
print("\n Average number of births:{:.0f}Times".format(df['total'].mean()))
print("\n Household distribution by number of girls")
df2 = pd.DataFrame(df['girls'].value_counts())

df2.index.name = 'Number of girls'
df2.columns = ['Number of households']

df2e = df2.copy()
df2e.index.name = 'Number of girls'
df2e.columns = ['number of couples']
df2e.plot(kind = 'bar', figsize = (8,5))

df2

Below are the outputs and comments from the code.

python

Born from a million couples,
Number of boys: 1000000
Number of girls: 999687

The number of boys is, of course, one million. The number of girls is almost one million.

python

Average number of births: 2 times

On average, if you give birth twice, you will have a baby boy. I'm convinced that the probability is 50%, but I didn't know in advance.

** Distribution of households by number of girls **

In about 50,000 households, half of the total, boys are born on the first birth and there are no girls. The probability is 50%.

The point that the total number of boys and girls is equal is that "50% of households have one boy and zero girls". When I thought about it intuitively, I overlooked this point.

And one girl will be about 25,000 households, two girls will be about 12,500 households, and so on. There is a 50% chance that a baby boy will be born per birth.

Finally, there was a couple who gave birth to 25 girls by the time they gave birth to a boy. thank you for your hard work.

The graph above shows this.

I didn't understand this quiz at first, but while writing the code, "When a boy is born, the couple will stop giving birth, and I'm kneading various things, but in the end, there is a 50% chance that which couple will give birth. Isn't it just that boys and girls continue to be born? "

A person with a good sense will immediately notice this fact, and a distribution image like the above graph will come to mind.

So the answer is

** "The male-female ratio in this country is 1: 1 (expected value)" **

Was the correct answer.