5% of the people of your age/heredity..

[gettoalok]

5% of the people of your age/heredity suffer from TB. A blood test was developed that correctly gives a positive test result in 80% of people with TB, and gives a false positive in 20% of the cases of people without TB. Suppose you take the test, and it is positive. What is the probability that you actually have TB, given the positive test result?

Does this problem use conditional probability? If so, please let me know how to use it in this problem?

*I have altered the text significantly enough to make it look completely different from the source text as I couldn't determine the author of this problem.

[esledge]

This is an overlapping set problem with two categories (TB Status and Test Result), best solved with a Double Set Matrix.

Use 100 as the total number of people, for ease of calculation. Thus, 5 have TB and 95 don't. Fill in the rest of the chart based on those numbers and the other percents given.

...........TB........no TB.........Total
Pos...(0.8)(5)...(0.2)(95)
Neg...(0.2)(5)...(0.8)(95)
Total.....5...........95.............100

Computing, this becomes

...........TB........no TB....Total
Pos.......4...........19.......23
Neg......1...........76........77
Total.....5...........95......100

So of all the positive test results (23 cases), 4 are True Positives. The probability is 4/23.