Probability that first born is a boy I had this question on an exam last week: there is a family, and they have $3$ children, you know that they have exactly $2$ boys and $1$ girl. What is the probability that the first born is a boy? 
Some people answered $1/2$ and others $2/3$, what do you think? We can't figure it out. 

The three different possibilities are BGB - BBG - GBB => Probability of a boy first is two thirds. 
Another way to look at it: call the children X,Y,Z, with Y and Z males, and X female. So what is the probability that X is first? It's 1/3, since they are all equally likely to come up first. So with probability 2/3 the first one is either Y or Z, i.e. a male.
