Let AAA and BBB be events such that P(A)=13P(A) = \frac{1}{3}P(A)=31, P(B∣A)=14P(B|A) = \frac{1}{4}P(B∣A)=41, and P(B∣Ac)=12P(B|A^c) = \frac{1}{2}P(B∣Ac)=21. What is the probability P(A∣B)P(A|B)P(A∣B)?
15\frac{1}{5}51
14\frac{1}{4}41
13\frac{1}{3}31
25\frac{2}{5}52