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Comment by x0054 | Hacker News Reader

The probability that you will roll 1 1 is indeed less then rolling 1 2 or 2 1, but that's only because you are allowing for twice as many acceptable outcomes.

The Wiki article you reference in your own code explains it well. The problem is in the assumptions made by the person answering a riddle. Just because you have a child, and it's a boy, and he is born on Tuesday, it does not mean that your next child is more likely to be a girl. If you agree with that statement, then the original answer must be false.

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The wiki article is not valid, since it considers a subtly different problem than the one I do. If you read the comment at the top of the code, you will see that I changed the question to be less ambiguous.

In the problem I pose, the person does not randomly come forward and tell me "I have a boy born on a tuesday". In my problem I ask random people who I know have two children if they have "at least on boy born on a tuesday" until someone says yes.

My python is really rusty, but if you convert this sudocode to python, you will see that the answer is 50/50. I'll write this up in Javascript when I have time. If you do this in Python, please post.

   girl = 0
   boy  = 0

   do 10000 times {
      child1Sex = randomSex;
      child1Day = randomDay;
      child2Sex = randomSex;
      child2Day = randomDay;
      if ( (child1Sex == "B" AND child1Day == "Tu") OR (child2Sex == "B" AND child2Day == "Tu") ) {
         if (child1Sex == child2Sex){
            boy++
         } else {
            girl++
         }
      }
   }

   print "Ratio of boys and girls is " + boy " : " + girl;

Here's my attempt in python: http://pastebin.com/tSDK1uRv

the range(0,10000) may not be correct, it might need to be 1,10000

Wow, works good. I should learn python :) But yeah, you were absolutely right! It was hard for me to figure out because I was trying to find a mathematical reason for this, and I was wrong. I finally figured it out mathematically. The way you posit the problem the probability that the asked parents have another boy is (1/2)-(1/7/2).

This is really counter intuitive, the open vs. closed probability set through me off. Hey, thanks for putting up with my stubbornness!

I whipped together something here, before I saw that someone else did it too: http://ideone.com/jyPOhs

It is the most counter-intuitive statistic problem I know (worse than Monty Hall), it trips everyone up at first.

No problem about the stubborness ;)

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