Here's a probability problem that stumps almost everyone: A person has two children. You are given that at least one is a boy born on a Tuesday. What is the probability that both children are boys? The answer is NOT 1/2 or 1/3. Let's break it down: 1/5

This is just bullshit. The probability in this case depends on why a person is giving me this specific information. If the «born on Tuesday» feature is selected in advance of knowing anything about the family, then the 13/27 is correct, but if the one giving the info has decided in advance to tell you the gender and the weekday of birth of a randomly selected out of two kids, then the correct answer is 1/2.

This is reminiscent of the Monty Hall problem, and how the conditions have to be clearly specified. If the host intentionally opened a door that he knew would reveal a goat, that is different from him opening a random door that happened to reveal a goat.