assumed that both children were considered while looking for a boy, the answer to question 2 is . However, if the family was first selected and then a random, true statement was made about the sex of one child in that family, whether or not both were considered, the correct way to calculate the conditional probability is not to count all of the cases that include a child with that sex. Instead, one must consider only the probabilities where the statement will be made in each case. So, if ALOB represents the event where the statement is "at least one boy", and ALOG represents the event where the statement is "at least one girl", then this table describes the sample space: So, if at least one is a boy when the fact is chosen randomly, the probability that both are boys is The paradox occurs when it is not known how the statement "at least one is a boy" was generated. Either answer could be correct, based on what is assumed. However, the "" answer is obtained only by assuming P(ALOB|BG) = P(ALOB|GB) =1, which implies P(ALOG|BG) = P(ALOG|GB) = 0, that is, the other child's sex is never mentioned although it is present. As Marks and Smith say, "This extreme assumption is never included in the presentation of the two-child problem, however, and is surely not what people have in mind when they present it." Modelling the generative process Another way to analyse the ambiguity (for question 2) is by making explicit the generative process (all draws are independent). The following process leads to answer : Draw equiprobably from Draw equiprobably from Discard cases where there is no B Observe The following process leads to answer : Draw equiprobably from Draw equiprobably from Draw index equiprobably from Observe Bayesian analysis Following classical probability arguments, we consider a large urn containing two children. We assume equal probability that either is a boy or a girl. The three discernible cases are thus: both are girls (GG) – with probability P(GG) = , both are boys (BB) – with probability of P(BB) = , and one of each (G·B) – with probability of P(G·B) = . These are the prior probabilities. Now we add the additional assumption that "at least one is a boy" = B. Using Bayes' Theorem, we find where P(A|B) means "probability of A given B". P(B|BB) = probability