Question: Compute probabilities for the following compound events:
We are given three new urns each containing seven red, five green, and three white balls, and two old urns each containing five red, three green, and seven white balls. The urns are identical except for an old or new date stamped beneath the base. If a single red ball is randomly drawn from one of these urns, was it most probably drawn from an old urn or a new urn? (Hint: For this exercise and the ones that follow, use Bayes's theorem.)