Suppose we have three boxes r (red), b (blue), and g (green). box r contains 30 apples, 4 oranges, and 3 limes, box b contains 1 apple, 1 orange and 0 limes, and box g contains 3 apples, 3 oranges, and 4 limes. consider the following process: a box is chosen at random with probabilities p(r) = 0.1, p(b) = 0.3, p(g) = 0.6, and a piece of fruit is selected uniformily at random from the box (with equal probability of selecting any of the items in the box), then what is the probability of selecting an apple? if we observe that the selected fruit is in fact an orange, what is the probability that it came from the green box?