The BG vs GB thing is difficult to understand. But easier to understand is that 50% of two child familes are mixed gender, while 50% are same gender. With 40 families having two children, 20 will have a boy and a girl, and 20 will have either two boys or two girls. Of the same gender familes, 50% (10) will be boy/boy and 50% (10) will be girl/girl. If you learn that a particular family has a daughter, then you know that family isn't one of the 10 families with two boys. This leaves 30 families, 20 of which (or 2/3) have one boy.
Likewise, for some reason the Monty Hall problem is hard to understand in three door form. But if you change the problem to 100 doors, and explain that Monty's assistant closes 98 bad doors, it's easier (at least for me) to see that the original guess had a 1/100 chance of being right, while the other door is 99/100 likely to be the right one.
Likewise, for some reason the Monty Hall problem is hard to understand in three door form. But if you change the problem to 100 doors, and explain that Monty's assistant closes 98 bad doors, it's easier (at least for me) to see that the original guess had a 1/100 chance of being right, while the other door is 99/100 likely to be the right one.