Each child has the same chance of being male as of being female. The sex of each child is independent of the sex of the other. The mathematical outcome would be the same if it were phrased in terms of a coin toss. First question Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls? Under the aforementioned assumptions, in this problem, a random family is selected. In this sample space, there are four equally probable events: Only two of these possible events meet the criteria specified in the question (i.e., GG, GB). Since both of the two possibilities in the new sample space {GG, GB} are equally likely, and only one of the two, GG, includes two girls, the probability that the younger child is also a girl is . Second question Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys? This question is identical to question one, except that instead of specifying that the older child is a boy, it is specified that at least one of them is a boy. In response to reader criticism of the question posed in 1959, Gardner said that no answer is possible without information that was not provided. Specifically, that two different procedures for determining that "at least one is a boy" could lead to the exact same wording of the problem. But they lead to different correct answers: From all families with two children, at least one of whom is a boy, a family is chosen at random. This would yield the answer of . From all families with two children, one child is selected at random, and the sex of that child is specified to be a boy. This would yield an answer of . Grinstead and Snell argue that the question is ambiguous in much the same way Gardner did. They leave it to the reader to decide whether the procedure, that yields 1/3 as the answer, is reasonable for the problem as stated above. The formulation of the question they were considering specifically is the following: Consider a family with two children. Given that one of the children is a boy, what is the probability that both children are boys? In this formulation the ambiguity is most obviously present, because it is not clear