Consider a bag with 4 red marbles, 2 green, and 5 blue. (a) If we select 2 marbles at random with replacement, what is the probability that they are of the same color? (b) If we select 3 marbles at random without replacement, what is the probability that they are of the same color? (c) When sampling with replacement, are the events that "two red marbles" and "2 green marbles" independent? Prove your answer. (d) Does your answer to (c) change if sampling without replacement? Explain.