If P(A) = 0.60, P(B) = 0.40, and P(B / A) = 0.60, then P(A / B) = 0.24.

Question

I thnk the asnwer is false am i Wrong?

Answer 1

P(B|A)=P(A∩B)/P(A) and P(A|B)=P(A∩B)/P(B).

P(A)=0.60, P(B)=0.40, P(B|A)=0.60, so P(A∩B)=0.60×0.60=0.36.

Therefore P(A|B)=P(A∩B)/P(B)=0.36/0.40=0.90.

So 0.24 is wrong.

A Venn diagram shows the problem more clearly. Two interlocking circles represent P(A) and P(B) and the region where they overlap is P(A∩B). This region belongs to both circles, and it is a proportion of each circle taken separately. As a proportion of the P(A) circle it represents P(B|A) and as a proportion of the P(B) circle it represents P(A|B). These proportions are what have been calculated above: the overlap region is a smaller proportion of the larger circle (P(A)) than of the smaller circle (P(B)).