Wait. What? The author says there can only be one BB but that there can be both GB and BG?
What he's doing here is saying that birth order functionally doesn't matter if the sibling is a boy, but it does matter if it's a girl. How is this correct?
If you keep comparing apples to apple you get:
Older Boy / Boy
Boy / Younger Boy
Older Girl / Boy
Boy / Younger Girl
And we're back to a 50% chance that the other child is a boy.
The Monty hall problem is based on the idea that you will always do the same thing in response to my choice aka he can always pick an open door. It's feels add to think about it in terms of what's already happens but seems more reasonable to say it in terms of something that will happen.
So if you say I will flip 2 coins and if I get zero heads I will flip again. So, if the first coin is a head second one either a head or a tail, but if it's a tail you know the second one is a head or I would have flipped again. Thus 3 options one of which is HH.
Assuming you used the same approach with the Tuesday boy problem, aka the first one can be BMTWTFSS or GMTWTFSS and the second one can be BMTWTFSS, GMTWTFSS but if I don't get a BT from the first or second try's I will pick again. Thus BT + BMTWTFSS or GMTWTFSS, OR BMTWTFSS or GMTWTFSS + BT minus a BT,BT which would otherwise be counted twice. Thus it's 14 + 13 options with 7 + 6 being BB. Which works out to 13/27.
Also I don't think the exact day of birth being Tuesday makes one bit of difference to the gender. For example, if you were to say the known boy was born crying, and the chance of this is 70%, it doesn't affect the gender of the other children. It's just useless trivia.
What he's doing here is saying that birth order functionally doesn't matter if the sibling is a boy, but it does matter if it's a girl. How is this correct?
If you keep comparing apples to apple you get:
And we're back to a 50% chance that the other child is a boy.