The Boy and Girl Paradox is a veridical paradox - a paradox that feels impossible on first sight, but when thought carefully, actually makes sense. 2 people, both either boy or girl in a 50% chance, where at least one of them is a girl. It is completely unknown which one is, or even if both are. The goal is to find the probability where both people are girls. To many people, the answer is 50% as you know one person is a girl, the only 2 options are for the second person to be either a boy or a girl. However, if we run a Monte Carol simulation, which is a test where you randomly generate a scenario and divide the matching scenarios with the total ones, the result will almost always approach 33.3...%, or as a fraction form, 1/3. The reason for this is that it is also possible for the second person to be a girl. In this case, there are 3 scenarios: boy and girl, girl and boy, and 2 girls. The scenario where both people are boys is rejected as none of them are girls. There is only 1 scenario where both people are girls, and a total of 3 scenarios, 1 matching and 2 not. Therefore, the answer is 1 matching scenario divided by 3 total scenarios, resulting in 1/3 or 33.333...%. Note that this is not the only version of the Boy and Girl paradox. In this version, the girl that you know is a girl can be any of the both people. In other versions, it is possible that you know the specific person that is a girl. In this case, that girl does not change the probability of the other person, resulting in an answer of 1/2, or 50%. For more information, go to https://en.wikipedia.org/wiki/Boy_or_girl_paradox to learn more complex versions.
To those who are confused about the difference of bg and gb: Although bg and gb both contains b and g, they are different because the both hold a 25% chance. If both of them were the same, then each of them holds a 12.5% chance, which contradicts the fact that there is a 25% chance for each pair as there are 4 pairs.
