(a) (8 points) If A and B are independent events, prove that A and Be are independent events. (b) (12 points) Consider the following random experiment: There are two urns - Urn 1 containing 5 red and 5 green balls and Urn 2 containing 2 red and 8 green balls. The experiment consists of first randomly selecting an urn and then randomly selecting 2 balls from the selected urn. (At each step of the experiment, all options are equally likely to be selected.) Given that both of the selected balls are red, what is the probability that Urn 2 was selected