Suppose that 0.1% of televisions produced by a factory are truly defective. The factory tests each...
Suppose that 0.1% of televisions produced by a factory are truly defective. The factory tests each television it produces. This test has the following performance:
• Among televisions that are truly defective, 99% were labeled defective by the test.
• Among televisions that are truly not defective, 98% were labeled not defective by the test.
The experiment is to randomly select a television produced by this factory.
(a) Compute the probability that this television is truly not defective.
(b) Given this television is truly not defective, compute the probability that it was labeled defective by the test.
(c) Compute the probability that this television is labeled defective.
(d) Given this television is labeled defective, compute the probability that it is truly defective.
Homework Answers
a) probability that this television is truly not defective =1-0.001=0.999
b)P(labeled defective given not defective)=1-0.98 =0.02
c)P(labeled defective)=P(defective and labeled defective)+P(not defective and labeled defective)
=0.001*0.99+0.999*0.02=0.02097
d)
P( truly defective given labeled defective)=P(defective and labeled defective)/P(labeled defective)
=0.001*0.99/0.02097=0.04721
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