(Imperfect Medical Tests) Suppose that 1% of a population contracted a certain disease. A
new diagnostic test has been developed. A diseased person is tested positive 97% of the
time. When the disease is absent, the test yields negative results with probability 95%. What
is the probability that a person tested positive has the disease? What is the probability that a
person tested negative does not has the disease?
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supplies 25% of the batches, vendor Y supplies 40% and vendor Z supplies 35%. There are
respectively 80%, 85% and 70% of the batches from vendors X, Y and Z are good.
(a) What is the percentage of good chemical batches in ABC Corporation?
(b) Given that a chemical batch is good, what is the probability that it is supplied by vendor
X?
(c) Given that a chemical batch is not good, what is the probability that it is supplied by
vendor X?
(d) If a chemical batch of ABC Corporation is selected at random, what is the probability that
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 Spring '09
 AnthonyChan
 Probability, Item bank, geologist

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