Can you please review the following text for grammatical errors? Thanks, MG.
When analyzing a prediction situation, always first consider various proportions comprising the underlying population. These proportions should guide your prediction of the next sample taken from the population.
Consider a case in which you are told that a person has two children and one of them is boy. What is the chance that the other one is a boy or a girl? 50% is not the answer here. What you need to understand here is the proportions of Boy-Boy, Boy-Girl, and Girl-Girl pairs in the underlying population. Note that in a pair the order of genders does indicate whether a child is younger or older than the other. In this case, we can estimate that the Boy-Girl pair is going to be approximately 50% of the population, with Boy-Boy and Girl-Girl each accounting for 25% of the population.
As such, if you are told that one child is boy, you should figure that the Girl-Girl pair is not part of the population of your interest. Your population is comprised of only Boy-Boy and Boy-Girl pairs, with Boy-Girl accounting for 2/3, and Boy-Boy accounting for 1/3 of the population. As a result, the chance that the second child will be girl is 2/3, with the chance of it being boy is only 1/3.