Please show all work and provide explanation so i understand. Thank you. An asse

Question

Please show all work and provide explanation so i understand. Thank you.

An assembler of computer routers and modems uses parts from two sources. Company A supplies 80% of the parts, and Company B supplies the remaining 20% of parts. From past experience, the assembler knows that 5% of the parts supplied by Company A are defective, and 3% of the parts supplied by Company B are defective. An assembled modem selected at random is found to have a defective part. What is the probability that the part came from Company A? Company B? (adapted from [Mendenhall and Sincich 2016], exercise 3.94)

Explanation / Answer

P(A) = 0.80, P(B) = 0.20

P(Defective | A) = 0.05 , P(Defective | B) = 0.03

a)

P(A | Defective) = P(A) * P(Defective | A) / [ P(A) * P(Defective | A) + P(B) * P(Defective | B) ]

= 0.80 * 0.05 / [ 0.80 * 0.05 + 0.20 * 0.03 ]

= 0.8696

b)

P( B | Defective) = P(B) * P(Defective | B) / [ P(A) * P(Defective | A) + P(B) * P(Defective | B) ]

= 0.20 * 0.03 / [ 0.80 * 0.05 + 0.20 * 0.03 ]

= 0.1304

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