A well-known probability riddle is “I have two children. [At least] one is a boy. What is the probability I have two boys?”; the answer is 1/3.
Richard shares a variation (imagined by Gary Foshee) which I find counter-intuitive: “I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?” (Assume uniformity over genders and days of the week.) This is easy to solve, using the method of your choice (1, 2).
Spoiler alert: the answer is 13/27. The addition of a seemingly useless piece of information makes a big difference, which surprised me.