Question

A diagnostic test has been developed for a rare disease, which affects 1 in 1000 people. suppose that the test gives a positive result 95% of the time when an individual has the disease, and gives a positive result 1% of the time when the individual does not have the disease. suppose an individual is tested and the result is positive. what is the probability that he/she has the disease?

Answer 1

@@@Answer is 0.50. @@@This is a little tricky, but you have to gather/calculate with numbers to figure this one out. If a person tests positive for the disease what is the chance that he or she actually has the disease is different from if the person actually has disease, what is the chance that they test positive for the disease. The order matters a lot.

Here are the numbers:
Assume there are a total of 100 people who actually have disease.
Since this is the 1%, there are total 10000 - 100 = 9900 people who don't have disease.
From the 100 diseased people, 99 test positive, and 1 negative.
From the 9900 non-diseased people, 99 test positive and 9801 negative.

People who test positive (99 + 99), the chance actually having disease is 99 / (99+99)