2. A flat six-sided die is thrown once. If a 3 or 4 appears, a ball is drawn from urn 1; otherwise, a ball is drawn from urn 2. Urn 1 contains five red and 15 white balls. Urn 2 contains eight red, four white, and eight black balls.

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

b) Find the probability that urn 2 was used given that a red ball was drawn.