Urn 1 contains 5 red, 4 white, and 6 blue marbles; Urn 2 contains 12 red, 2 white, and 3 blue marbles; and Urn 3 contains 20 red, 1 white, and 1 blue marble. One of the three urns is chosen at random, and then one marble is drawn at random from that urn

.a. Determine the probability that a red marble is drawn.

b. Determine the probability that a red marble is drawn, given that Urn 2 was chosen.

c. What is the probability that Urn 2 was chosen, given that a red marble was drawn?

d. What is the probability that Urn 1 was chosen, given that a red marble was NOT drawn?

e. What is the probability that Urn 3 was NOT chosen, given that a red marble was NOT drawn?