Suppose that 5% of the general population has a disease and the test for the disease is accurate 80% of the time. What is the probability of testing positive for the disease?

Question

Konnor Simpson

Mathematics

28 June, 05:05

Suppose that 5% of the general population has a disease and the test for the disease is accurate 80% of the time. What is the probability of testing positive for the disease?

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Franco Reese · Answer 1

If anyone in the population is tested randomly and they have a 5% chance of having the disease. The test is 80% accurate.

The question isn't very clear, assuming we are looking for the chance of having the disease and testing positive

The probability of having the disease = 5% = 0.05

The probability of testing positive (when you have it) = 80% = 0.80

To add probabilities together you multiply them:

0.05 * 0.80 = probability of testing positive for the disease when you have it

0.05 * 0.80 = 0.04 = 4%

The probability of someone out of random getting picked, and then the probability that that person will get tested positive for the disease and actually have it, is 4%