I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
Would you believe 0.481481481… (or, more accurately and informatively, 13/27)?
This problem has easier roots in the famous Two Child Problem, originally phrased thusly:
- Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
- Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
The answer to the first is 1/2. The answer to the second is traditionally 1/3, though it can be 1/2 depending on how you found out one child is a boy.
The fact that one of my children was born on a Tuesday is actually germane to the problem. You can see the full solution and some history here. The article points out that your intuition is likely to be correct in real life where you would know why something like Tuesday is included, but math puzzles like this are designed to eliminate that knowledge.