The school of Science and Engineering at a local university regularly purchases

Question

The school of Science and Engineering at a local university 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. (a) Draw a tree diagram to represent the possible outcomes when a single component is selected at random. (b) 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

P(company A) = 0.6

P(company B) = 0.4

P(defective | compnay A) = 0.02

P(defective | compnay B) = 0.01

b)

i) P(company A and defective) = P(defective | compnay A) * P(compnay A) = 0.02 * 0.6 = 0.012

ii) P(defective) = P(defective | compnay A) * P(compnay A) + P(defective | compnay B) * P(compnay B)

= 0.02 * 0.6 + 0.01 * 0.4

= 0.016

iii) P(company A | defective) = P(defective | compnay A) * P(compnay A) / P(defective)

= 0.02 * 0.6 / 0.016

= 0.75

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