An experiment includes selecting an urn with the following probabilities that Urn 1, Urn 2, or Urn 3 will be selected: 1/2, 1/4, and 1/4, respectively. Urn 1 haves 5 brown marbles and 13 clear marbles. Urn 2 contains 15 brown marbles, 11 clear marbles and 9 red marbles. Urn 3 contains 7 brown marbles, 12 clear marbles and 6 red marbles.
A marble is then selected from the chosen urn. Determine the probability that Urn 3 was selected, given that marble chosen was clear?
a) 0.1200
b) 0.2144
c) 0.1600
d) 0.3165
e) 0.4800