Posted by **Anonymous** on Sunday, September 23, 2007 at 11:20pm.

This is a statistics problem.

A laboratory test for the detection of a certain disease give a positive result 5 percent of the time for people who do not have the disease. The test gives a negative result 0.3 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 2 percent of the population.

What is the probability that a person selected at random would test positive for this disease?

For this one, I got 0.0194, so 1.94% but I wasn’t sure if the answer is correct.

What is the probability that a person selected at random who test positive for the disease does not have the disease?

This one was confusing to me… I got 0.71637, or 71.637% but I doubt this is right. Please help!

- math -
**drwls**, Monday, September 24, 2007 at 9:20am
Consider the four possibilities and their probabilities.

has disease and tests positive:

(0.02)x(0.997)= 0.0199

has disease but tests negative:

(0.02)x(0.003)= 0.0001

has no disease and tests negative:

(0.98)x(0.95) = 0.9310

has no disease but tests positive:

(0.98)x(0.05) = 0.0490

Note the probabilities they add up to 1.000, as they should.

The answer to the first question (positive test probability) is

0.0199 + 0.0490 = 0.0689

The answer to the second question is:

0.0490/(0.0199+0.0490)= 0.7112

This is a rather large ratio of "false positives" and comes about because the disease is rare (2% of population) and there are many more false positives than "true" positives

- math -
**Anonymous**, Monday, September 24, 2007 at 12:09pm
That makes perfect sense. Thank you very much.

- math -
**Anon Ymous**, Friday, November 12, 2010 at 8:04pm
hey, we just did this problem in class today...this is from the ap stats 1197 free response prep...the first question's ans. is 0.06894 and the second ques.'s ans. is 0.710763

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