Richard Henage

Empiricism is the belief that knowledge derives from sensory experience, or, by some definitions, experiment. However, empiricism itself can show that it is not the best tool for a given scenario. This article provides an example of when this happened to me. The Two-Child Puzzle is a logic problem. The version I first heard goes like this: > I know my co-worker has exactly two kids that each have an independent 50/50 chance of being a boy or a girl. I ask her if at least one of her kids is a boy. She tells me that is correct. The question is: From my perspective, what is the probability that the other one is a boy as well? The answer, I immediately supposed, was 1/3, while the trick was that most readers would guess 1/2. I posed the question to a friend and asked him what he thought. He thought it was clearly 1/2, and said multiple times throughout our ensuing discussion that he was very confident. I tried a variety of tactics to persuade him, initially using pure logic. However, the complexity of language and my inexperience as a teacher made us run in circles, as he would continue to state something like "but what we know about one of the kids can't change the probability of the other" or "if she brought a boy to work one day, instead of telling you she had a boy, you would think that the other kid had a 1/2 chance of being a boy instead of 1/3". I attempted to use more empirical tactics. First, I used coins to demonstrate the puzzle. They happened to come up with the "girl" answer the first three times, which is more likely if the probability is 1/3 of being a boy than 1/2 of being a boy, yet the method seemed unreliable and my friend was highly skeptical. Then, I created a spreadsheet with 1000 rows using random values, showing different averages like "both girls", "both boys", "one or more boys", "kid 1 is a boy", and "kid 2 is a boy". I showed that when all results of "both girls" were factored out, the spreadshee