Quantitative Literacy Practice Exam

For a couple with three biological children, what is the probability of having one girl and two boys?

1. 1/8

2. 1/4

3. 1/2

4. 3/8

The correct answer is: 1/8

To find the probability of having one girl and two boys in a family with three biological children, we can use the principles of probability and combinatorics. When each child is born, assuming there is an equal chance of being a boy or girl, each birth can be treated as a Bernoulli trial with two possible outcomes: boy (B) or girl (G), each with a probability of 1/2. For three children, the possible combinations of genders can be represented as sequences of B and G. The total number of combinations of three children is calculated as \(2^3\) (since there are two possibilities for each child), which equals 8. The combinations are: BBB, BBG, BGB, GBB, GGB, GBG, BGG, and GGG. To find the specific combination of having one girl and two boys, we need to determine how many ways this can occur. The combinations for one girl and two boys can be represented as: BBG, BGB, and GBB. There are three distinct combinations that can produce one girl and two boys. Since we have established there are a total of 8 possible combinations, and among these there are 3 that satisfy the condition