SOLUTION: 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

Question 1192755: 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 i. Represent this information in a tree diagram ii. What fraction of all the components are rejected? iii. What fraction of the components rejected are actually not defective? iv. What fraction of those not rejected are defective

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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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
i. Represent this information in a tree diagram
ii. What fraction of all the components are rejected?
iii. What fraction of the components rejected are actually not defective?
iv. What fraction of those not rejected are defective
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(ii)    Fraction of all rejected components = 0.05*(1-0.04) + (1-0.05)*0.07 = 0.1145.    ANSWER

        The formula is self-explanatory.



(iii)   Fraction of the rejected components that are actually not defective = (1-0.05)*0.07.    ANSWER

        The formula is self-explanatory.

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