Suppose a family has  children, one of which is a boy. What is the probability that both children are boys?

Two events, A and B are considered to be independent if event A has no effect on the probability of event B, i.e. P(B|A) = P(B).

Events are independent if P(A Intersect B) = P(A) * P(B)

Outcomes: BG, GB, BB, GB

Let A = an event of having both boy chil, B = an event of having at-least one boy child.

A={(B,B)},
B={(B,G), (G,B), (B,B)}
                              1
                             ---
         P(A Intersect B)     4        1
P(A|B) = ---------------  = -----  =  ---
	     P(B)             3        3
                             ---
			      4