Solution
Two Children
Show the problem again
A family has two children. You learn that at least one of them is a boy. What is the probability that both are boys? (Assume boys and girls are equally likely and genders are independent.) Express as a fraction.
Worked solution
The answer is 1/3. The equally likely gender orderings are BB, BG, GB, GG. Conditioning on "at least one boy" eliminates only GG, leaving three equally likely outcomes of which one is BB. So the probability is 1/3, not 1/2, because "at least one is a boy" is weaker information than "the elder is a boy."
Source: The two-children problem, posed by Martin Gardner in Scientific American (1959). Statement written for AxiomIQ.