Three machines A, B, and C produce 50%, 30%, and 20% of the entire factory output, respectively.

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Three machines A, B, and C produce 50%, 30%, and 20% of the entire factory output, respectively. The reject rates for the machines are 3%, 4%, and 5%, respectively.

(a) Represent the individual probabilities using a probability tree.

(b) What is the probability that a randomly selected piece is defective?

(c) What is the probability that a randomly selected defective part is from machine A?

(d) What is the probability that a randomly selected part is from machine A or defective?

(e) What is the probability that a randomly selected part is from machine B and is not defective?

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