1. 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 it will not be rejected. If a component is not defective there is 7% probability that it will be rejected. a) What fraction of all the components are rejected? b) What fraction of the components rejected are actually not defective? c) What fraction of those not rejected are defective?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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1. 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 it will not be rejected. If a component is not defective there is 7% probability
that it will be rejected.
a) What fraction of all the components are rejected?
b) What fraction of the components rejected are actually not defective?
c) What fraction of those not rejected are defective?
Transcribed Image Text:1. 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 it will not be rejected. If a component is not defective there is 7% probability that it will be rejected. a) What fraction of all the components are rejected? b) What fraction of the components rejected are actually not defective? c) What fraction of those not rejected are defective?
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