Final answer:
The probability of a couple having two boys and two girls out of four children is calculated using combinations. There are 6 ways to have this outcome out of 16 total possible gender combinations for four children, resulting in a probability of 3/8 or 37.5%.
Step-by-step explanation:
The question involves calculating the probability of a couple having two boys and two girls out of four children. We use the concept of combinations to determine the number of ways to achieve this outcome. Since having a boy or a girl is equally likely, each child has a 1 in 2 chance of being a boy or a girl. For two boys and two girls, we will have a combination of BBGG, in no particular order. There are 6 ways to arrange two boys and two girls, which are BBGG, BGBG, BGGB, GGBB, GBGB, and GBBG. The probability is computed as the number of desired outcomes divided by the total possible outcomes. To calculate the total number of possible outcomes for four children, we raise 2 (the number of possible genders per child) to the power of 4 (the number of children), giving us 16 possible different gender combinations. The probability of having two boys and two girls is therefore:
Probability = (Number of ways to have 2 boys and 2 girls) / (Total number of possible outcomes)
Probability = 6 / 16
Probability = 3 / 8 or 0.375
Thus, the probability that the couple has two boys and two girls is 3/8 or 37.5%.