1. The problem statement, all variables and given/known data I'm told that of n couples, each of whom have at least one child, with couples procreating independently and no limits on family size, births single and independent, and for the ith couple the probability of a boy is p_i and of a girl is q_i with p_i + q_i = 1. 1. Show the expected family size if the ith couple stop when have had both sexes is 1/(p_iq_i) - 1. 2. If all n couples stop when have children of both sexes, what is the expected number of girls. 2. Relevant equations E(X) = Sum(i=1..n) E(X|A_i) P(A_i) E(X|A) = Sum(over x) xP(X=x|A) 3. The attempt at a solution So for 1 I've got: Let X be the number of births until a girl and boy A1 = boy born 1st A2 = girl born 1st E(X) = E(X|A_1)P(A_1) + E(X|A_2)P(A_2) = (p_i/q_i) + (q_i/p_i) = 1/(p_iq_i) -2 Do I add 1 as I'm considering 2 births not 1? For 2: I'm not too sure how to go about this at all, I can use the second formula with X being the number of girls and A being that both sexes are born, but how do I know P(X=x|A)? Earlier in the question I calculated the expected family size if the family stopped after a boy or a girl. Thanks.