I am watching this YouTube video on conditional probability example by a university professor. He gives 2 examples:
What is the probability of $2$ children being girls if we were told at least one of them is a girl (answer = $1/3$)
What is the probability of $2$ children being girls if we were told the oldest one is a girl (answer = $/1/2$)
I understood both examples, he explained quite well. My question is: is this really true in life ? e.g. Let's say a couple has their first child,
- If first child was a girl then they have 50% chance of 2nd child will be girl
- If first child was a boy then they have 33% chance of 2nd child will be girl
Does this really happen ? Have we checked the data related to births to verify its correctness or we are sure formula works because we believe probability has been proved useful over 3 centuries or we just do it this way because it is mathematical formula ?
or is it just a mathematical formula ?