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 disease is present if the test result comes back positive

Question

Mathematics

Ramiro Peck

22 December, 17:59

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 disease is present if the test result comes back positive

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Callie · Answer 1

4.48%

Step-by-step explanation:

The first thing is to take into account all the possible events as follows

If D is disease present

If ND is disease not present

If P is a positive test

If F is test false

From the statement we have the following information:

P (D) = 0.05% = 0.005

P (P | D) = 99% = 0.99

P (P | ND) = 4% = 0.04

The total number of% positive tests would be the sum of the positive tests when the disease is% present and the positive tests when the disease is not present that it false positives.

Therefore the equation would be like this:

P (P) = P (P | D) * P (D) + P (P | ND) * (1 - P (D))

Replacing the values:

P (P) = 0.99 * 0.005 + 0.04 * (1 - 0.005)

P (P) = 0.00495 + 0.0398

P (P) = 0.04475

What it means is that the probability that they are positive is 4.48%