SOLUTION: supposed that a test for a disease correctly gives results for 97% of those having the disease and correctly gives negative results for 94% of those who dont haave the disease. SUp

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Question 62600: supposed that a test for a disease correctly gives results for 97% of those having the disease and correctly gives negative results for 94% of those who dont haave the disease. SUppose also that the incidence of the disease is 1%. Of the people who test positive what percentage actually have the desease
Answer by 303795(602) (Show Source):
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In this problem there are four possible scenarios
Scenario 1: A person has the disease and tests positive
Scenario 2: A person has the disease and tests negative
Scenario 3: A person doesn't have the disease and tests positive
Scenario 4: A person doesn't have the disease and tests negative
Scenario 1: 97% of the 1% with the disease
of the population.
Scenario 2: 3% of the 1% with the disease
of the population.
Scenario 3: 6% of the 99% without the disease
of the population.
Scenario 4: 94% of the 99% without the disease
of the population.
The people in groups 1 and 3 will test positive ie 0.0097 + 0.0594 = 0.0691
Of these 0.0097 actually have the disease so the percentage is