A 10-sided die is rolled and depending on the result a ball is then chosen from one of three boxes. If the roll results in a 1, 2, or 3 a ball is drawn from box A, if the roll results in a 4 or 5 a ball is drawn from box B, and if the roll results in a 6, 7, 8, 9, or 10 a ball is drawn from box C. If box A contains 4 red, 8 white, and 5 black balls, box B contains 6 red and 11 black balls, and box C contains 7 white and 10 black balls:
a) What is the probability that you draw a red ball?
b) What is the probability that you draw a black ball that does not come from box B?
c) What is the probability that you draw a white ball that comes from box A?
d) What is the probability that you draw a red ball given that you drew the ball from box B?
e) What is the probability that you drew from box C given that the ball is black?