Girl Boy
A family has two children. What is the probability that the first is boy given that one of the children is a girl?
martha2A: Feb. 8, 2015, 11:41 p.m.
martha2A: Feb. 8, 2015, 11:54 p.m.
oops! that's only A intersect B. Is it 4/9?
lewenchiu: Feb. 9, 2015, 12:30 a.m.
alexlevine: Feb. 9, 2015, 12:43 a.m.
I think it's confusing because the problem isn't very clear if exactly one child is a girl or at least one child is a girl. If exactly one is a girl, it would be 1/2. If at least one is a girl, it would be 1/3.
JCampos: Feb. 9, 2015, 4 a.m.
the answer is 1/3. We already know that one of them is for sure a girl. However we don't know what the other child might be. The outcomes are O = {GG, GB, BG}. We can see that a boy can be the first child born one time out of three possible ways. {BB} cannot be an outcome because we know that the family already has one girl as a child.
martha2A: Feb. 9, 2015, 8:26 a.m.
Yeah it's 1/3. I overthought it and did extra work.