A couple has two female children. What is the probability that their next child will be male? This question is more than just a curiosity, it has significant implications for the future of this family.
How would you answer this question? Most would probably say that the probability is 50%, but that’s only if you look at this question in isolation.
This question becomes much more complicated when you take other factors into account. For example, what if one of the children was a girl because they used pre-implantation genetic diagnosis to determine the sex of the fetus, and therefore only a girl could have been born? Or what if one of the children was a girl because they had X-Y sperm, and all other possible zygotes were XX? Then the next child could very well be a boy!
The answer to this question also depends on whether or not you consider gender identity in your answer.
Consider all possible outcomes
When you’re thinking about probabilities, it can be helpful to think about all the possible outcomes of a situation, and how many of those outcomes are positive and negative.
For example, when thinking about the probability that your next child will be male if you have two female children, there are four possible outcomes:
Your next child is male Your next child is female Your next children are both female Your next children are both male
Only the fourth outcome is positive — that is, your next child will be a boy. The first three are all negative — your next child will be a girl.
The other important thing to note here is that there’s no chance your next child will be both male and female! Only one of these two traits will be passed on from you.
Only two female children
If a couple has two female children, the chance of their next child being male is 50%. This is because couples that have two female children have an equal chance of having a male child or a female child.
This is because they have already had two daughters, and the chance of having another daughter is equal to the chance of having a son. So theoretically, they are as likely to have a boy as a girl!
However, this does not take into account twins. If the couple in question had twin girls, then the probability of having a boy next would be 50%. This is because there is an equal chance of having either sex as there was for girls.
Twins are unique individuals, though.
One female and one male child
If a couple has one female and one male child, the chance that their next child will be male is 50%. This is because there is a 50% chance that the next child will be gender specific based on the sex of the previous children.
This is due to what’s called nondisjunction, which is when chromosomes don’t separate during cell division. This results in cells containing too many or too few chromosomes.
When this happens in a sperm or egg, it can result in a pregnancy that includes more or less than two sexes.
However, this isn’t the case for every couple. There have been cases of couples having three children of one sex and then having a child of the other sex later on. This proves that it is possible for there to be more than two sexes in the family after two have already been established.
Two male children
Now, let’s look at the case where a couple has two male children. What is the probability that their next child will be female?
Once again we can use the binomial distribution. This time we will use n = 2, p = 0.5, and x = 1 to find the probability of a female child.
The probability of two male children is 0. Thus, 1 – this probability is the probability of a female child.
So if a couple has two male children, then there is a 75% chance that their next child will be female!
This may seem surprising at first but remember that gender is not determined by the sex of your previous children. A couple can have two girls and still have a chance to have a boy in their next pregnancy.
Combining probabilities
So far, you have learned how to find the probability of one event, and how to find the probability of two independent events. Now you will learn how to find the probability of two events happening simultaneously.
Probabilities can be combined if the events are independent of each other. Independent just means that the outcome of one event does not affect the outcome of the other event.
For example, if we know someone is a man, then we know they are not a woman, and vice versa. Being a man is not dependent on whether or not someone is pregnant. These two properties are independent of each other.
Since we already know someone is a man or a woman, knowing that they are pregnant does not change that fact. These two facts are independent of each other.
Understanding conditional probability
Conditional probability is the term for understanding the likelihood of one event happening given that a specific event has already occurred.
For example, you may hear that people who drink alcohol are at higher risk of certain health problems, such as cancer. However, that does not mean that drinking alcohol guarantees you will get cancer-that is not true!
The reason this fact is mentioned is because there is a strong association between the two events-drinking alcohol and getting cancer. The probability of getting cancer if you drink alcohol is higher than if you do not drink alcohol.
Conditional probability tests are a part of the Aptitude Test in the Workplace (AT-W) exam. AT-W exam takers need to understand what conditional probability is, how to calculate it, and how to apply it in situations.
The paradox of the twins
A curious phenomenon related to gender probability is the paradox of the twins. It refers to the fact that a woman who has a child with a partner has a higher chance of having twin babies if she has another child with the same partner.
Why? Because chances are that her next child will be a boy, and twinning is more likely when conceiving a boy. Since there is already one more chance of having a boy, twinning is even more likely.
Of course, this only applies if the couple has no plans to have any more children. If they want to have another child, then there’s no reason why they shouldn’t — even if it’s going to be another girl.
Genetic testing helps determine sex of fetus
A growing number of people are choosing to find out the sex of their fetus very early. You can find out as early as four to five weeks after conception, which is before you would find out the gender of your baby at an ultrasound.
How is this possible? With advances in fetal DNA testing, you can either get a blood test or collect urine to test the fetal DNA. This then gets sent to a lab where they determine the sex of the fetus.
Increasingly, doctors are reporting that they are receiving babies of both sexes at the same rate, indicating that pre-natal DNA testing is working.
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