Box 1 haves 8 red marbles and 4 white marbles. Box 2 haves 10 red marbles and 2 white marbles. The two boxes are chosen at random with equal probabilities. Answer each of following by showing your work. In each case, make a probability tree diagram that clearly shows each outcome and its corresponding probability.
a) If a marble is selected at random, what is the probability that it is a red?
b) If the marble selected is red, what is the probability that it comes from box 1?