| I know Gary, the person who presented this, and I was there when it happened. He fully intended this to ignite the argument it has. Firstly, as presented it is clearly ambiguous. It is intended to be ambiguous, but in such a way that people who are familiar with the original version will get suckered into believing that it's well formed. Secondly, if presented precisely, the answer usually given is either 13/27 or 1/2, depending on which version. Finally, this is like the Monty Hall problem all over again. There are people arguing vehemently and without listening at all, demonstrating clearly that they are excellent at missing the point. In case you're wondering, here's one statement and answer. Suppose on knock on people's doors and ask - Do you have exactly two children? If they answer no, I move on. If they answer yes I then ask - Is at least one of them a boy born on a Tuesday? If they say no, I move on. If they look surprised and say "Yes," what is the probability that they have two boys? Answer: 13/27. Yes, it really is. If you replace the second question with "Is at least one of them a boy with red hair, left-handed, plays piano, was born on Tuesday, and has a cracked left upper incisor" then if the answer is "Yes" then the probability of both children being boys is almost exactly 50%. If, instead, you replace the second question with "Is at least one a boy" then the probability of two boys is 1/3. Finally, suppose you see a parent that you know has two children in the park with a boy. Now the probability of two boys is 50%, because, assuming uniform probabilities, having two boys makes it more likely you see them with a boy. tl;dr: It's hard, and depends precisely on the assumptions you make. |