An 8-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 a ball is drawn from box B, and if the roll results in an 5, 6, 7, or 8 a ball is drawn from box C. If box A contains 6 blue, 3 pink, and 2 purple balls, box B contains 5 blue and 6 purple balls, and box C contains 8 pink and 3 purple balls:
a) What is the probability that you draw a pink ball?
b) What is the probability that you draw a blue ball from box B?
c) What is the probability that you draw a purple ball that does not come from box C?
d) What is the probability that you draw a blue ball given that you drew the ball from box A?
e) What is the probability that you drew from box B given that the ball is purple?
Academic requirements:
• Your work should be submitted in the formats outlined for each question in the assignment.