This is the most famous “wait, what?” in elementary probability, and it’s here because it exposes a subtlety that even people who can compute conditionals fluently walk straight into.
Setup, with the usual simplifications (each child independently a girl or boy with probability 1/2 — lesson 4 says we should justify that; here it’s a modeling assumption, and a fine one):
A colleague has exactly two children. Before you learn anything, there are four equally likely possibilities, ordered by birth:
GG GB BG BB (each with probability 1/4)
You ask her directly: “Is at least one of them a girl?” — and she truthfully answers “yes.”
Given that answer, what’s the probability that both children are girls?
Conditioning (lesson 2) tells you the mechanical move: throw away the worlds inconsistent with what you learned, and re-count inside what remains. Do that carefully — the intuitive shortcut “well, then the other one is 50/50” is doing something different, and one of them is wrong.
Answer the question above. Then, before you reveal the solution, consider a second scenario and ask yourself whether it’s the same question: you run into her at the park with one of her children — a daughter. What’s the probability both are girls now?