(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

Solution

Given that , Factor A = 2Factory C

Factory B = 7 * Factory C

P(defective by A) = 0.032

P(defective by B) = 0.035

P(defective by C) = 0.058

Proportion of production by Factor A,B and C respectively = A+B+C =1

2C+7C+C = 1 so, C = 1/10 ,A = 2/10, B = 7/10

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

P(defective from factory B) = 0.035/0.0367 = 0.9537

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