Navigating the realm of chance, we dissect the likelihood of gender sequences among siblings. What determines the sex of a second-born if the first is a son? Simple math illuminates the odds of diverse family configurations, from all-boys to a blend, as we delve into the probabilities shaping a family’s blueprint.

1. What is the probability that a couple’s second child will be a boy if their first child is a boy?
The probability of the first child being a boy is 1/2, and the probability of the second child being a boy is also 1/2.
2. What is the probability that a couple’s two children will both be boys?
Since the likelihood of the first child being a boy is 1/2 and the likelihood of the second child being a boy is also 1/2, therefore 1/2 multiplied by 1/2 equals 1/4. Hence, the probability of having two boys is 1/4.
3. What is the probability that a couple’s first child is a boy and the second child is a girl?
The chance of the first child being a boy is 1/2 and the chance of the second child being a girl is also 1/2, so 1/2 times 1/2 is 1/4. This means the probability of having a first child as a boy and the second as a girl is 1/4.
4. What is the probability that a couple’s two children will be one boy and one girl?
The probability of having a boy is 1/2 and the probability of having a girl is also 1/2, thus the chance of having one boy and one girl is 1/4. However, since the order can either be boy-girl or girl-boy, there are two possible combinations. So, 1/4 times 2 equals 1/2. Therefore, the probability of having two children, one of each gender, is 1/2.
5. What is the probability that all three children of a couple will be boys?
The probability of the first child being a boy is 1/2, the second child being a boy is also 1/2, and the third child being a boy is again 1/2. Therefore, 1/2 multiplied by 1/2 multiplied by 1/2 equals 1/8. Thus, the probability of having three boys is 1/8.
6. What is the probability that a couple’s first child is a boy, the second child is a girl, and the third child is a boy?
The likelihood of the first child being a boy is 1/2, the second child being a girl is 1/2, and the third child being a boy is 1/2 as well. So, 1/2 times 1/2 times 1/2 is 1/8. Consequently, the probability of having three children with the first being a boy, the second a girl, and the third a boy is 1/8.
7. What is the probability that a couple’s three children will be two boys and one girl?
The probability of having a boy is 1/2, and the probability of having a girl is also 1/2. Considering these probabilities, the order of births could be as follows: first a boy, second a boy, third a girl; or first a boy, second a girl, third a boy; or first a girl, second a boy, third a boy. There are three possible combinations to have two boys and one girl. Therefore, multiplying 1/2 by 1/2 by 1/2 and then by 3 gives us 3/8. Thus, the probability of having three children with exactly two boys and one girl is 3/8.