A 6-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 a ball is drawn from box A, if the roll results in a 2 or a 3 a ball is drawn from box B, and if the roll results in a 4, 5, or 6 a ball is drawn from box C. If box A contains 1 red, 6 white, and 3 black balls, box B contains 6 red and 4 black balls, and box C contains 3 white and 7 black balls:

a) What is the probability that you draw a black ball?

b) What is the probability that you draw a red ball from box A?

c) What is the probability that you draw a black ball that does not come from box B?

d) What is the probability that you draw a white ball given that you drew the ball from box C?

e) What is the probability that you drew from box A given that the ball is black?

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