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

Matilda

Mathematics

29 November, 05:23

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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Jordan Mahoney · 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%