Suppose a famin with two children is selected at random, and the genders of the children are noted in the order of their birth (f for female, m for male}. Assume that the possible outcomes {f fm,mf,mm} are all equally likely. (a) A family tells us that the rst child is female. Given this information, what's the probability that both children are female? (b) Another family tells us that at least one of the children is female. Given this information, what's the probability that both children are female? {c} Assume that, if a child is female, then her name is Katie with some small probability 11 independently of the gender and naming of the other child, and that no boys are named Katie. Now, a third family tells us that they have at least one child named Katie. Given this information, what '5 the probability that both children are female