One in two hundred people in a population have a particular disease. A diagnosis test gives a false positive 3% of the time, and a false negative 2% of the time. Ross takes the test and the report comes positive. Find the probability that Ross has the disease.

brasocas6

brasocas6

Answered question

2022-08-09

One in two hundred people in a population have a particular disease. A diagnosis test gives a false positive 3% of the time, and a false negative 2% of the time. Ross takes the test and the report comes positive. Find the probability that Ross has the disease.

Answer & Explanation

heiftarab

heiftarab

Beginner2022-08-10Added 10 answers

The probability that the person has the disease and the test is negative is not 2 / 100, but 1 / 200 2 / 100 = 1 / 10000.
The likelihood that the person has the disease and the test is positive is 2 / 100 98 / 100 = 196 / 10000 = 0.0196, not 98 / 100.
The likelihood that the person does not have the disease and test is positive is 199 / 200 3 / 100 = 597 / 20000 = 0.02985.
So the likelihood of having a positive test is then 196 / 10000 + 597 / 20000 = 9989 / 20000 = 0.04945.

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