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)=(P(B\cap A))/(P(A))\implies P(B\cap A)=0.2\cdot0.9=0.18`

Similarly,

`P(A\mid B)=(P(A\cap B))/(P(B))=(0.18)/(0.3)=0.6`