An electrician regularly purchases a particular type of electrical component. 60

Question

An electrician regularly purchases a particular type of electrical component. 60% are purchased from company A, and 40 % are from Company B.2% of those supplied by company A and 1% of those supplied by Company B are known to be defective. The components are identical and thoroughly mixed on receipt. If a component is selected at random i) What is the probability that this component was supplied by company A and was defective? (ii) Calculate the probability that the component was defective. (iii) Given that the component was defective, what is the probability that it was supplied by company A.?

Explanation / Answer

One component is slecected at random so probability of it getting selected from Company A = 0.6 and from company B = 0.4

P( Defective if from A company) = 0.02 and P ( defective if from B company) = 0.01

(i) P( Componenet was supplied by company A and was defective) = 0.6 * 0.02 = 0.012

(ii) P ( component is defective) = P(defective if from Company A) + P ( defective if chosen from company B) =

0.02 * 0.6 + 0.01 * 0.4 = 0.016

(iii)Given that component is defective probabiity that it was supplied by Company A

= (0.6* 0.02) / ( 0.6 * 0.02 + 0.4 * 0.01) = 0.012/0.016 = 3/4 = 75%

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