Urn I contains five black and seven white balls. Urn II contains six black, five white, and

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Urn I contains five black and seven white balls. Urn II contains six black, five white, and three red balls. Roll a fair die.

If the die is a one, three, or five, randomly select a ball from urn I. However, if the die is a two, four, or six, randomly select a ball from urn II.

(a) Determine the probability that the ball is black by drawing a tree diagram.

(b) Determine the probability that the ball is black using the Rule of Total Probability.

(c) Suppose that a randomly chosen ball is black. What is the probability that the ball came from urn I?

(d) Suppose that a randomly chosen ball is red. What is the probability that the ball came from urn I? urn II?

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