Another google problem

Imagine you are in a world where all the parents want to have a boy, and every parent keeps having a children until they have a boy, then they stop giving birth. If the number of male population in this world is given by p p , and the number of female population is given by q q . What is the value of p q \frac{p}{q} .

Continuation of previous question ,


The answer is 1.

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7 solutions

Adit Mohan
Apr 11, 2014

each couple will have 1 son. mean boys per couple =1.
probability of of having 0 girls = 1/2(0.5 chance that first is boy).
probability of having 1 girl = 1/4 (0.5 first is girl *0.5 second is boy).
and so on.
mean girls per couple= s u m i = 1 i n f i n i t y sum_{i=1}^{infinity} i/ 2 i + 1 2^{i+1} =1.
thus boys/girls =1


Mayank Holmes
Apr 9, 2014

it was a mere guess man!

@Mayank Holmes , man, this question could have been put up in another way, lyk if the parents want girls, so the answer must remain the same. There are only two cases, either they wish for a boy or a girl, and since the probabilities for both are same, therefore no. of girls = boys . Therefore p/q=1

A Former Brilliant Member - 7 years, 2 months ago

haha I just thought "Well for every and girl there must have been a boy and girl pair, so I guess as it goes off to infinity only the couples would matter."

Milly Choochoo - 7 years, 2 months ago

Ignoring the circumstances, each time a couple is going to have a child, the probability that the child is a boy is 1 2 \frac{1}{2} So having a child n n times, the expected number of boys is n 2 \frac{n}{2} and the expected ratio is 1 : 1 1:1

Notice that the probability of having a boy is independent of whether the previous child is a boy or not.

Brock Brown
Jun 21, 2015

What this problem is asking is, "If you want to flip a coin until you get heads and you repeat the experiment for a long time, what's the head to tails ratio?" Just because you're ending the experiment when you see heads doesn't mean the probability of heads has changed.

Python 3.4:

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from random import choice
from time import time
p = 0
q = 0
def intercourse():
    # this is actually how babies are made
    boys = 0
    girls = 0
    boy = False
    while not boy:
        boy = choice((True, False))
        if boy:
            boys += 1
        else:
            girls += 1
    return boys, girls
end = time() + 10
# make babies for 10 seconds
while time() < end:
    new_boys, new_girls = intercourse()
    p += new_boys
    q += new_girls
print("p/q is about", round(p/q, 2))

Thumbs up for cool GIF!!

Beakal Tiliksew - 5 years, 11 months ago

You should ask for "expected" value of p/q...

As opposed to the unexpected value of p q \frac{p}{q} ?

Brock Brown - 5 years, 11 months ago
Metta Ong
Apr 17, 2014

Using probability,where probability of getting girl and boy is equal

P ( G e t t i n g B o y s ) P ( G e t t i n g G i r l s ) = P ( B ) + P ( G B ) + P ( G G B ) + . . . P ( G ) + P ( G G ) + P ( G G G ) + . . . = 0.5 + 0. 5 2 + 0. 5 3 + . . . 0.5 + 0. 5 2 + 0. 5 3 + . . . = 1 \frac{P(GettingBoys)}{P(GettingGirls)} = \frac{P(B) + P(GB) + P(GGB) + ...}{P(G) + P(GG) + P(GGG) + ...} = \frac{0.5 + 0.5^2 + 0.5^3 + ...}{0.5 + 0.5^2 + 0.5^3 + ...} = 1

Max B
Apr 11, 2014

the\quad probabilities\quad for\quad both\quad boy\quad and\quad girl\quad are\quad the\quad same....hence\quad the\quad answer\quad 1

how to use latex

Max B - 7 years, 2 months ago

Log in to reply

close the latex in \ ( \ ) , that should help

Beakal Tiliksew - 7 years, 1 month ago

Log in to reply

Don't use latex for normal text, it is clear in its own way

Beakal Tiliksew - 7 years, 1 month ago

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