A balanced die is thrown once. If a 4 appears, a ball is drawn from urn 1;

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.