You're on a game show. Behind one of 3 doors is a car; behind the other two are goats. You pick door 1. The host (who knows what's behind each door) opens door 3 to reveal a goat, then asks if you'd like to switch to door 2. Should you switch?
A neighbour says "I have two children, and at least one of them is a boy." What is the probability that both children are boys?
How many people do you need in a room before the probability that at least two share a birthday exceeds 50%? (Ignore leap years.)