A balanced die is thrown once. If a 4 appears, a ball is drawn from urn 1;

Question:

A balanced die is thrown once. If a 4 appears, a ball is drawn from urn 1; otherwise, a ball is drawn from urn 2.

urn 1 contains two red, four white and six black balls. Urn 2 contains one red and five black balls.

a. Find the probability that a red ball is drawn.

b. Find the probability that urn 1 was used given that a red ball was drawn.

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