Manipal Entrance Test 2015 Math Paper

Let u1 and u2 be two urns such that u1 contains 3 white, 2 red balls and u2 contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from urn u1 and put into u2. However, if tail appears, then 2 balls are drawn at random from u1 and put into u2. Now, 1 ball is drawn at random from u2. Then, probability of the drawn ball from u2 being white is