Three children, at least one boy
A family has three children, each independently equally likely to be a boy or a girl.
Given that at least one of the three is a boy, what is the probability that all three are boys? How does the answer change if you are told the oldest child is a boy?
Show a hint
Write out all eight equally likely orderings of three children and cross out the ones each piece of information rules out.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.