Please help. (20 points) We have 3 factories producing fuses. The probability a

Question

Please help.

(20 points) We have 3 factories producing fuses. The probability a fuse is defective is 0.001 if it was produced by factory A. The probability a fuse is defective is 0.006 if it was produced by factory B, and the probability a fuse is defective is 0.002 if it was produced by factory C. We have a large lot of fuses, 20% of the fuses in the lot were produced in factory A, 30% of the fuses were produced in factory B, and 50% of the fuses were produced in factory C. We select a fuse in the lot randomly. What is the probability it is defective? 3.

Explanation / Answer

X - fuse is defective
P(X) = P(X|A)P(A) + P(X|B)P(B) +P(X|C)P(C)
= 0.001 * 0.20 + 0.006*0.30 + 0.002*0.50
= 0.003

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