Hacker News Reader

Comment by stavrianos | Hacker News Reader

I feel like the fact that I can choose how many times to play might throw things? If I were more likely to stop after non-arousing image than after an arousing one, what will that do statistically?

View on HN

Even if you decide to stop having kids after your first son, the population of males / females should be split evenly, so I don't think it would make a difference.

I don't think that's true.

  public class test {
      public static void main( String[] args ) throws Exception {
          int boys = 0, girls = 0;
          for (int i = 0; i < 1000000; i++) {
              boolean isBoy = (Math.random() >= 0.5);
              while (! isBoy) {
                  girls++;
                  isBoy = (Math.random() >= 0.5);
              }
              boys++;
          }
          System.out.println( "Boys: " + boys + "\nGirls: " + girls );
      }
  }

I don't know what output you're getting, but this is what I got:

  $ java test
  Boys: 1000000
  Girls: 996931
  $ java test
  Boys: 1000000
  Girls: 1001605
  $ java test
  Boys: 1000000
  Girls: 1001656
  $ java test
  Boys: 1000000
  Girls: 999473
  $ java test
  Boys: 1000000
  Girls: 1000645

Looks pretty even to me.

Besides, if you compute the girls/boy ratio mathematically, you get

  0/2 + 1/4 + 2/8 + 3/16 + 4/32 + 5/64 + ...

which does converge to 1.

This was recently released as an old Google interview question and sparked some controversy.

This MathOverflow page [1] is a good (opinionated) summary. The best answer's author believes that with finitely many families the ratio actually doesn't work out evenly, but does converge to 50/50 with infinitely many families.

[1] http://mathoverflow.net/questions/17960/google-question-in-a...

Well, that's pretty obvious. If it involves an infinite sum, but you only have n people, you don't quite get to that infinity-th guy ;)

The answer suggested that even the expected value is never going to be 1/2 but instead something similar to 1/2-1/(4k) for k families which stop having children after the first boy. So, it's a bit more sophisticated than that involving situations where you test the average percentage of an infinite number of islands with k families each.

That's specifically talking about the expectation of a ratio though. The expectation of the number of girls is always equal to the number of boys, even for finite families.

Expectation of a ratio != ratio of expectations.

Maybe the clearest way to see it is that the expected number of boys is one (obviously--there's always exactly 1), and the expected number of girls is also one (1/2 + 1/4 + ...) since the prob. of (at least) one girl is 1/2, and the prob. of a second girl is 1/4, and so on.

I agree. This the first explanation that's made me fully understand and accept this problem.

Hmm. The handful of times I tried it I always got a smaller number for the girls than the boys. Just goes to show sample size is important... :)

Reply on news.ycombinator.com