Question: A balanced die is thrown once. If a 4 appears, a ball is drawn from urn 1 otherwise; a ball is drawn from urn 2. Urn 1 contains four red, three white, and three black balls. Urn 2 contains six red and four white balls.

a.) Find the probability that a red ball is drawn.

b.) Find the probability that urn 1 was used given that a red ball was drawn.