(2 points) Factories A, B and C produce Factory A produces 2t many computers as

Question

(2 points) Factories A, B and C produce Factory A produces 2t many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.032, the probability that a computer produced by factory B is defective is 0.035, and the probability that a computer produced by factory C is defective is 0.058. A computer is selected at random and it is found to be defective. What is the probability it came from factory B? Answer:

Explanation / Answer

P(computers produces by factory C) = 0.1

.P(computers Produces by factory A) = 0.2

P(computer Produces by   factory B) = 0.7

P(defective) = 0.1 * 0.058 + 0.2 * 0.032 + 0.7 * 0.035 = 0.0367

P(produces by factory B | defective) = P(defective | produces by factory B) * P(computer Produces by   factory B)/P(defective) = 0.035 * 0.7/0.0367 = 0.668

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