The two-child puzzle and how you learned it
A family has two children, each independently a boy or girl with probability .
Version A: you are told "at least one of the two is a boy." Version B: you knock on the door, a randomly chosen one of the two children answers, and it is a boy. In each version, what is the probability that both children are boys?
Show a hint
Write the four equally likely families (BB, BG, GB, GG) and ask, under each version, how likely you were to receive the information you got. The likelihood is where the versions differ.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.