22Bayes' theorem on urns

Urn A holds 3 red and 2 blue balls; urn B holds 1 red and 4 blue. An urn is chosen at random and a ball drawn: it's red. Find $\displaystyle P(\text{it came from urn A})$.

Use Bayes' theorem: weight each urn's chance of giving red by how likely that urn was picked. P(A∩red)=3/10, P(B∩red)=1/10, so P(red)=4/10. Then P(A|red) = (3/10)/(4/10) = 3/4.