A quality-control program at a plastic bottle production line involves inspectin

Question

A quality-control program at a plastic bottle production line involves inspecting finished bottles for flaws such as microscopic holes. The proportion of bottles that have such a flaw is only 0.0002. If a bottle has a flaw, the probability is 0.995 that it will fail the inspection. If a bottle does not have a flaw, the probability is 0.99 that it will pass the inspection. Suppose a bottle is chosen at random. (a) What is the probability that it has a flaw AND that it fails inspection? Select ] (b) What is the probability that it fails inspection? Select ] (c) Given that the bottle failed inspection, what is the probability that the bottle has a flaw? Select ] 101 97% 17.5% 0199% 1.95% 32.46%

Explanation / Answer

Ans:

Given that

P(flaw)=0.0002

P(not flaw)=1-0.0002=0.9998

P(fail the inspection/flaw)=0.995

So,P(pass the inspection/flaw)=1-0.995=0.005

P(pass the inspection/not flaw)=0.99

So,P(fail the inspection/not flaw)=1-0.99=0.01

a)P(flaw and fails the inspection)=P(fail the inspection/flaw)*P(flaw)=0.995*0.0002=0.000199 or 0.0199%

b)P(fails the inspection)=P(fails the inspection/flaw)*P(flaw)+P(fail the inspection/not flaw)*P(not flaw)

=0.995*0.0002+0.01*0.9998

=0.000199+0.009998

=0.010197 or 1.0197%

c)P(flaw/fail the inspection)=P(fail the inspection/flaw)*P(flaw)/P(fail the inspection)

=0.995*0.0002/0.010197

=0.019516 or 1.95%

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