Question

For Test Strip A:

If the person has the disease: strip will show positive result 95% of the time / negative result 5% of the time. If the person does NOT have the disease: strip will show positive result 10% of the time / negative result 90% of the time If a person tests positive, they take test again. It turns out that 15% of people who take the test again test positive again. If everyone is tested, what percentage of the population has the disease.

Answer 1

For a diseased person

Positive result = 95% of time

Negative result = 5 % of time

for a non diseased person

Positive Result = 10%

Negative Result = 90%

Here the person test postiive ,90% who take the test again

who take the test again test positve again = 15 % of time

so here if the percentage of population that have the disease = x

then,

P(Positive people tested positve again) = 0.15 = P(Non Diseased person who were found positive earlier were found positive again) + P(Diseased person who were found positive earlier were found positive again

P(Non Diseased person who were found positive earlier were found positive again) = (1-x) * 0.10 * 0.10

P(Diseased person who were found positive earlier were found positive again = x * 0.95 * 0.95

0.15 = (1-x) * 0.01 +  0.9025 x

0.15 = 0.01 - 0.01x + 0.9025 x

0.8925 x = 0.14

x = 0.157

so here 15.7% population has the disease.