The problem in the image is what I need help with. Can somebody write out each s

Question

The problem in the image is what I need help with. Can somebody write out each step and explain what every thing means? I am having trouble understanding what every thing in here means.

3.94 Modem supplier. An assen modems uses parts from two sources. Company A sup- plies 80% of the parts and company B supplies the remain- ing 20% of the 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. Which of the two companies is more likely to have supplied the defective part?

Explanation / Answer

Ans:

Given that

P(A)=0.8

P(B)=0.2

P(defctive/A)=0.05

P(defective/B)=0.03

First find,P(defective) using total law of probability:

P(defective)=P(defective/A)*P(A)+P(defective/B)*P(B)

=0.05*0.8+0.03*0.2=0.046

Now,use Bayes rule to find:

P(A/defective)=P(defective/A)*P(A)/P(defective)=0.05*0.8/0.046=0.8696

P(B/defective)=P(defective/B)*P(B)/P(defective)=0.03*0.2/0.046=0.1304

As,P(A/defective) is greater than P(B/defective),So,company A is more likely to have supplied the defective part.

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