Final answer:
The probability that a family of 4 children will have the same number of boys and girls is 3/8.
Step-by-step explanation:
The probability that a family of 4 children will have the same number of boys and girls can be calculated using the concept of combinations. The sample space consists of all possible combinations of boys and girls, which is given by 2^4 = 16. Now, we need to find the number of favorable outcomes where there are equal numbers of boys and girls. There are 6 combinations where we can have 2 boys and 2 girls: BBGG, BGBG, BGGB, GGBB, GBGB, and GGGB. Therefore, the probability is 6/16, which simplifies to 3/8.