Question

In a manufacturing plant, machine A produces 10% of a certain product, machine B produces 40% of this product, and machine C produces the remaining portion of this product. 5% of machine A products are defective, 12% of machine B products are defective, and 8% of machine C products are defective. a) [4pts] Draw a probability tree for this question. Clearly indicate the symbols and the probabilities on each branch. b) [6pts] The company inspector has just sampled a product from this plant and has found it to be defective. Determine the probability that the sampled product was produced by machine C.

          In a manufacturing plant, machine A produces 10% of a certain product, machine B produces 40% of this product, and machine C produces the remaining portion of this product. 5% of machine A products are defective, 12% of machine B products are defective, and 8% of machine C products are defective.

a) [4pts] Draw a probability tree for this question. Clearly indicate the symbols and the probabilities on each branch.
b) [6pts] The company inspector has just sampled a product from this plant and has found it to be defective. Determine the probability that the sampled product was produced by machine C.

Added by Joel H.

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