Final answer:
The theoretical probability of a family with two children having one boy and one girl is 1/2, considering the four equal possible combinations of two children.
Step-by-step explanation:
The question asks about the theoretical probability of a family with two children having one boy and one girl.
To determine this, we consider all possible combinations of two children, which are BB (two boys), GG (two girls), BG (first a boy, then a girl), and GB (first a girl, then a boy).
Since there are four possible outcomes, and two of them result in one boy and one girl (BG and GB), the probability of having one boy and one girl is 2 out of 4, which can be reduced to 1/2.
Therefore, the correct answer is c. 1/2.