Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
The probability is 1/3.
There are initially 4 possibilities: girl-girl, girl-boy, boy-girl and boy-boy. Since at least one of them is a boy (but we don’t know if it’s the first or second child), we can rule out the girl-girl combination.
Only one out of the 3 combinations is boy-boy, so we get a probability of 1/3.