SOLUTION: A and B are events defined on a sample space, with P(A) = 0.5 and P(A and B) = 0.2. Find P(B | A).

Formula for conditional probability:


                   P(First AND Second)       P(Second AND First) 
P(First|Second) = ---------------------  =  ---------------------
                       P(Second)                 P(Second)

Note: the events might be in either order on the top since AND 
is commutative, but the denominator is always the probability 
of what is given, that is, what is after the vertical line "|".

with P(A) = 0.5 and P(A and B) = 0.2. 

Find P(B|A)  

Here the First = B and the Second = A

                   P(Second AND First) 
P(First|Second) = ---------------------
                       P(Second)

           P(A and B)     0.2
P(B|A) = ------------- = ----- =   = 0.4
              P(A)        0.5

Edwin