Question

isco 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 comes back negative if the disease is present

Answer 1

Answer:

0.8894 is the probability that the test result comes back negative if the disease is present .

Step-by-step explanation:

We are given the following in the question:

P(Disco Fever) = P( Disease) =

$P(D) = \dfrac{1}{2}\times 1\% = 0.5 \times 0.01 = 0.005$

Thus, we can write:

P(No  Disease) =

$P(ND) =1 - P(D)= 0.995$

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

$P(TP | D ) = 0.99$

P( false-positive) = 4%

$P( TP | ND) = 0.04$

We have to evaluate the probability that the test result comes back negative if the disease is present, that is

P(test result comes back negative if the disease is present)

By Bayes's theorem, we can write:

$P(ND|TP) = \dfrac{P(ND)P(TP|ND)}{P(ND)P(TP|ND) + P(D)P(TP|D)}\\\\P(ND|TP) = \dfrac{0.995(0.04)}{0.995(0.04) + 0.005(0.99)} = 0.8894$

0.8894 is the probability that the test result comes back negative if the disease is present .