8* A medical researcher estimates that 2% of a population is infected with a rare disease which for this problem we will assume is accurate. The procedure used for testing for this disease is 90% accurate. So, if one has the disease, the test will indicate that 90% of the time, and if the person doesn't have the disease, the test will indicate that 90% of the time. Of course, what this means is that the test will give a false positive result 10% of the time. If a person is picked at random and tested: (a) What is the probability that the person tests positive? (b) What is the probability that if a person tested positive for the disease he or she actually had the disease?

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8* A medical researcher estimates that 2% of a population is infected with a rare disease which for
this problem we will assume is accurate. The procedure used for testing for this disease is 90%
accurate. So, if one has the disease, the test will indicate that 90% of the time, and if the person
doesn't have the disease, the test will indicate that 90% of the time. Of course, what this means
is that the test will give a false positive result 10% of the time. If a person is picked at random
and tested:
(a) What is the probability that the person tests positive?
(b) What is the probability that if a person tested positive for the disease he or she actually had
the disease?
Transcribed Image Text:8* A medical researcher estimates that 2% of a population is infected with a rare disease which for this problem we will assume is accurate. The procedure used for testing for this disease is 90% accurate. So, if one has the disease, the test will indicate that 90% of the time, and if the person doesn't have the disease, the test will indicate that 90% of the time. Of course, what this means is that the test will give a false positive result 10% of the time. If a person is picked at random and tested: (a) What is the probability that the person tests positive? (b) What is the probability that if a person tested positive for the disease he or she actually had the disease?
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