There are 3 urns containing coins. Urn I contains 3 gold coins, urn II contains 1 gold coin and 1 silver coin, and urn III contains 2 silver coins. An urn is selected and a coin is drawn from the urn. If the selected coin is gold, what is the probability that the urn selected was urn I?
Use (a) a probability tree and
(b) Bayes' formula to find the probabilities.