A company produces machine components which pass through an automatic testing ma

Question

A company produces machine components which pass through an automatic testing machine. 5% of the components entering the testing machine are defective.However, the machine is not entirely reliable. If a component is defective there is 4% probability that will not be rejected. If a component is not defective there is 7% that will be rejected. (a) What fraction of the components rejected are actually not defective? (b) What fraction of the components are rejected? (c) What fraction of those rejected are defective? Round off your answer to four decimal place

Explanation / Answer

Ans:

Given that

P(defective)=0.05

P(not defective)=1-0.05=0.95

P(not rejected/defective)=0.04

P(rejected/defective)=1-0.04=0.96

P(rejected/not defective)=0.07

First find:

P(rejected)=P(rejected/defective)*P(defective)+P(rejected/not defective)*P(not defective)

=0.96*0.05+0.07*0.95=0.1145

Now.we have to find:

a)P(not defective/rejected)=P(rejected/not defective)*P(not defective)/P(rejected)

=0.07*0.95/0.1145=0.5808

b)P(rejected)=0.96*0.05+0.07*0.95=0.1145

c)P(defective/rejected)=P(rejected/defective)*P(defective)/P(rejected)

=0.96*0.05/0.1145=0.4192

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