@norfolksheep@Landeur@RupertLowe10 It was 74% in 2021 (before the biggest wave of migration in history). By now it is probably much closer to 2/3 of the population.
@notSeaSmoke@filip_ma@GLabsPlus@Math_files I've done a lot of thinking about this problem over the last 2 hours. I also did a small python simulation.
I really cannot wrap my head intuitively around the 14/27, but I have come to the conclusion that you are correct.
@notSeaSmoke@filip_ma@GLabsPlus@Math_files It isnโt twice as likely on its own, but once you condition on Btu at least once, it becomes twice as likely in this new conditional โprobability spaceโ.
Put more simply, being told that Btu happened at least once, biases us towards this case more than towards the others.
@notSeaSmoke @MrPJ3000 @Math_files The day of the week is irrelevant. You are making the question more difficult than it needs to be for no reason, and then you end up making a mistake somewhere. Show me the full calculation you did to get 14/27.
@notSeaSmoke @MrPJ3000 @Math_files These probabilities are the same because the events are independent. That what independence means.
If A and B are independent then P(A and B given B) = P(A).
In this question, A is the event that the unknown child is a girl. B is the event that the known child is a boy (given).
@notSeaSmoke @MrPJ3000 @Math_files But the question tells you that one event (one child is a boy) has already happened, meaning it is no longer random.
If S1 and S2 are the sexes of child 1 and child 2, the questions is not asking P(S1=B and S2=G), it is asking P(S1=B and S2=G given S1=B)=P(S2=G)=0.5