P(A|B) = .1, P(B) = .7, P(A|B') = .5. Find P(B|A)

How do you do this?

P(A|B)=P(A intersection B)/P(B)=0.1 given
P(B)=0.7 given
So P(A intersection of B)=0.1*0.7=0.07

Similarly, P(A|B')=P(A intersection B')/P(B')=0.5 given
P(B')=1-P(B)=1-10.7=0.3
So P(A intersection B')=0.5*0.3=0.15

A is the disjoint union of (A intersection B) and (A intersection B')
So P(A)=P(A intersection B)+P(A intersection B')
=0.07+0.15=0.22

P(B|A)=P(B interscetion A)/P(A)
=0.07/0.22

P(B|A) = P(A|B) P(B) / P(A)