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2 months ago

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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

1 answer:

Svet_ta [12.7K]2 months ago

5 0

Answer:

0.8894 represents the likelihood of a negative test result given that the disease is present.

Step-by-step explanation:

We are provided 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 express:

P(No Disease) =

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

P(Test Returns Positive with disease present) = 0.99

$P(TP | D ) = 0.99$

P( false-positive) = 4%

$P( TP | ND) = 0.04$

We need to assess the likelihood of a negative test result when the disease is indeed present, i.e.,

P(test result being negative while disease is present)

According to 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 returns negative when the disease exists.

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