I have a homework question

three urns have the distributions of ball shown below

Black White Green

U1 7 3 10

U2 3 5 2

U3 5 7 3

Suppose a ball is selected at random from U1. A fair die is then tossed and if a number less than three appears the ball is placed in U2, otherwise the ball is placed in U3. You walk into the room and select U1 or U2 at random and select a ball.

A) which color are you most likely to select?

B) If the ball you selected is black, what is the probability a green ball was selected from U1?