Question

Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result is positive?

0.1106

0.0523

0.0056

0.0448

Answer 1

Solution:

Given:

P( Disco Fever) = P( Disease) = P(D) = (1/2) of 1% = 0.5 * 0.01 = 0.005

then

P( No  Disease) = 1 - 0.005

P(ND) = 0.995

P(Test Positive given the presence of the disease) =0.99

P(TP | D ) = 0.99

Also we have:

P( false-positive) =4%

P( TP | ND) = 0.04

We have to find:

P( the test result is positive) =.........?

That is:

P(TP) =..........?

P(TP) = P(TP | D ) X P(D) + P( TP | ND) X P(ND)

P(TP) = 0.99 X 0.005 + 0.04 X 0.995

P(TP) = 0.00495 + 0.03980

P(TP) = 0.04475

P(TP) = 0.0448