To determine the probability of the woman's fourth child being a girl, we can make use of basic concepts in probability theory.
The probability of any event can be thought of as the number of ways the event can occur divided by the total number of possible outcomes. When it comes to the gender of a newborn child, we often use a simplified model where there are only two possible outcomes: the child can either be a boy or a girl. This model assumes that there are no other influencing factors and each outcome is equally likely.
Therefore, in this simplified model, the probability of having a boy is 50%, and the probability of having a girl is also 50%, often expressed as a decimal, 0.5 for each.
An important principle in probability is that of independent events. If the gender of one child has no effect on the gender of another, then the events are said to be independent. In the case of having children, it is generally considered that the genders of separate births are independent events.
Given the situation that the woman has already three boys, the gender of the fourth child is still an independent event and its probability is not influenced by the genders of the previous children. Therefore, the fact that the woman already has three boys does not affect the probability of the fourth child being a girl.
So the probability that the woman's fourth child will be a girl remains the same as it would be for any single birth, which is 50% or 0.5. It's important to remember that past outcomes do not change the probabilities for future independent events in this context.
In conclusion, despite the woman's history of having boys, the probability that her fourth child will be a girl is still 0.5, or 50%.
