Let events A_{1},...,A_{k} form a partition of the space
S such that Pr(A_{j})>0 for j=1,...,k, and let B be any
event such that Pr(B)>0. Then for i=1,...,k,

Pr(A_{i}|B) = Pr(A_{i})*Pr(B|A_{i}) / Sum for j=1 to k of
Pr(A_{j})*Pr(B|A_{j}).

The source of this problem is the May 1997 issue of the *Actuarial Review*.
Applying this theorm:

B=boy selected

A_{1}=boy added

A_{2}=girl added

g=number of girls before baby is added.

Pr(A_{2}|B) = (1/2)*(2/(3+g)) / [(1/2)*(2/(3+g)) + (1/2)*(3/(3+g))] = 0.4

Michael Shackleford, A.S.A.