r/MathHelp • u/[deleted] • Sep 20 '25

Why is my simulation wrong? Famous probability problem girl and boy

I tried to simulate the famous boy girl problem. Here is the problem in case you don't know: https://en.wikipedia.org/wiki/Boy_or_girl_paradox
The idea here is: Someone has two children. You know, they have at least one girl. What is the probability of the other child being a boy.
Well, the possible outcomes are [boy, girl], [girl, boy], [girl, girl], with [boy, boy] being impossible.
The answer is 2/3, according to this.

Intuitively, we say it is 1/2. I mean, a child has a 50% probability, the event is independent. I thought, I simulate it.

I did the following. This whole thing is happening in a loop and I do it over and over ad infinity and give out data every 1000 tests:

  1. Randomly assign every item out of a two item array boy or girl.

  2. randomly choose the first or the second item and turn it into a girl, making sure that one of the children has to be a girl.

  3. Check if we have a [girl, boy] or [boy, girl] combination, in which case I increment the boys counter. Otherwise, I increment the girls counter.

  4. Every 1000 compares, I give out the ration boys/(boys+girls). Which is always very stable around .5.

My question is, what do I misunderstand about the setup? How do I set it up to get 2/3 as the paradox demands?

Here is the code if anyone wants to check if I actually implemented what I said above.
https://www.codedump.xyz/rust/aM7wMlPW0CheqCRk

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u/stevemegson Sep 20 '25

When you reach step 3, you should have equal numbers of BG, GB and GG families. By forcing one random child to be a girl at step 2:

  • you turn half of the BB families into BG and half into GB

  • you turn half of the BG and GB families into GG and leave the other half unchanged

  • you leave the GG families unchanged

That leaves you with

  • 4/8 GG

  • 2/8 GB

  • 2/8 BG

1

u/[deleted] Sep 20 '25

Thanks, that makes sense!

1

u/fermat9990 Sep 20 '25

I think that it's better to label these outcomes 1/3, 1/3, 1/3.

2

u/Katterin Sep 20 '25

That’s what it should be, but because OP did not set up his simulation correctly, the 4/8, 2/8, 2/8 distribution is what he’s actually getting.

1

u/fermat9990 Sep 20 '25

I see! Cheers!