Calculating the probability of having at least one boy and one girl in a family:
To calculate the probability of a family having at least one boy and one girl, we need to consider the different possible combinations of children in a family. Since each family has 4 children, there are a total of 16 different combinations of children that can be born in a family.

Calculating the probability of having all boys or all girls in a family:
- The probability of having all boys in a family is 1/16 (as there is only 1 way to have all boys).
- The probability of having all girls in a family is also 1/16 (as there is only 1 way to have all girls).

Calculating the probability of having at least one boy and one girl in a family:
- To calculate the probability of having at least one boy and one girl, we need to subtract the probability of having all boys or all girls from 1.
- Probability of having at least one boy and one girl = 1 - (Probability of having all boys + Probability of having all girls)
- Probability of having at least one boy and one girl = 1 - (1/16 + 1/16) = 1 - 1/8 = 7/8

Expected number of families with at least one boy and one girl:
- Out of 128 families with 4 children each, the expected number of families with at least one boy and one girl can be calculated by multiplying the total number of families by the probability of having at least one boy and one girl.
- Expected number of families = 128 * (7/8) = 112
Therefore, we can expect 112 out of 128 families with 4 children each to have at least one boy and one girl.