Question

Suppose P(A) = 0.9, P(B) = 0.3, and P(B|A) = 0.2. What is P(A|B) ?

Answer 1

By definition of conditional probability,

$P(B\mid A)=\dfrac{P(B\cap A)}{P(A)}\implies P(B\cap A)=0.2\cdot0.9=0.18$

Similarly,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.18}{0.3}=0.6$