Final answer:
The probability of having 3 children of one sex and 4 children of the other sex in a family of 7 is approximately 27.34%.
Step-by-step explanation:
To calculate the probability of having 3 children of one sex and 4 children of the other sex in a family of 7, we need to use combinatorics. There are 7 ways to choose the 3 children who will be of one sex, and for each of those choices, there are 4 ways to choose the remaining 4 children who will be of the other sex. So the total number of favorable outcomes is 7C3 * 4C4 = 35 * 1 = 35. There are a total of 2^7 = 128 possible outcomes for the family. Therefore, the probability of having 3 children of one sex and 4 children of the other sex is 35/128, which simplifies to approximately 0.2734, or 27.34%.