I came across this example in a class I am taking and I am having a bit of trouble wrapping my head around the answer that was provided. The question is: "Your neighbor has 2 children. You learn that he has a son, Joe. What is the probability that Joe's sibling is a brother?"

So which formula better fits this question? (B = boy, G = girl)

1. Four possible combinations of having two children: BB, BG, GB, GG

Since there is already Joe, GG is not a option. So, P(BB) / P(BB,BG,GB) = (1/4) / (1/4 1/4 1/4) = 1/3

A 1/3 chance Joe's siblong is a brother.

2. Three possible combinations of having two children: Boy and Boy, Boy and Girl (regardless of order), and Girl and Girl.

Since there is already Joe, GG is not an option. So, P(BB) / P(BB, B and G) = (1/3) / (1/3 1/3) = 1/2

A 1/2 chance Joe's sibling is a brother