Using Bayes' theorem, calculate the probability that a person who has had a positive test for a disease actually has the illness. Typically the test gives a correct positive result 90.0% of the time when a person has the illness. and gives an incorrect positive result 1.0% of the time when the person does not. Assume that 0.3% of the population has the illness, and the person who is tested was selected at random without necessarily showing any symptoms. Give your answer as a percentage with one digit after the decimal point. How would your answer in the previous part change if only people who showed symptoms typical of the illness were tested. and why?

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Using Bayes' theorem, calculate
the probability that a person who
has had a positive test for a
disease actually has the illness.
Typically the test gives a correct
positive result 90.0% of the time
when a person has the illness.
and gives an incorrect positive
result 1.0% of the time when the
person does not. Assume that
0.3% of the population has the
illness, and the person who is
tested was selected at random
without necessarily showing any
symptoms. Give your answer as
a percentage with one digit after
the decimal point.
How would your answer in the
previous part change if only
people who showed symptoms
typical of the illness were tested.
and why?
Transcribed Image Text:Using Bayes' theorem, calculate the probability that a person who has had a positive test for a disease actually has the illness. Typically the test gives a correct positive result 90.0% of the time when a person has the illness. and gives an incorrect positive result 1.0% of the time when the person does not. Assume that 0.3% of the population has the illness, and the person who is tested was selected at random without necessarily showing any symptoms. Give your answer as a percentage with one digit after the decimal point. How would your answer in the previous part change if only people who showed symptoms typical of the illness were tested. and why?
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