Problem 1. Three types of identicallylooking apples grow in a tree: (I) with 1 black seed, (H) with 1 black seed and 2 brown seeds, and (III) with 1 black seed and 3 brown seeds. Fifty percent of apples are of type (I), thirty percent are of type (II) and twenty percent are of type (III). When you eat an apple, you encounter seeds one by one, with each seed equally likely to be encountered rst. (a) If you pick an apple from this tree, what is the probability that the rst seed you encounter is black? (b) Given the information that you picked an apple from the tree and the rst seed you encountered was black, what is the probability that this was an apple of type (I)