[pico]

let's say you're in a isolated tropical island (with enough people living there to use probability to estimate) with 0.1% (1/1000) of catching gonorrhea. there is a gonorrhea test avaliable at the island clinic with false positive rate of 5%. people are tested at random, regardless of whether they are suspected of having gonorrhea. A patient's test is positive. What is the probability of the patient being stricken with gonorrhea?

[DrunkenLullaby]

Assuming that somebody that actually has the disease will always (100%) test positive, I get 1.9627% as the answer to your question.

[Ganchrow]

Originally Posted by DrunkenLullaby

Assuming that somebody that actually has the disease will always (100%) test positive, I get 1.9627% as the answer to your question.

You got it.

This is a classic application of Bayes Theorem:

P(gonorrhea|test positive)
= ^{P(test positive|gonorrhea)*P(gonorrhea)}/_{P(test positive)}
= ^{P(test pos|gonorrhea)*P(gonorrhea)}/_{(P(test pos|gonorrhea)*P(gonorrhea) + P(test pos|no gonorrhea)*P(no gonorrhea))}

If we assume a false negative rate of 0 (not specified by the OP) then P(test positive|gonorrhea) = 1. Hence:

= ^{(1 * 0.1%)}/_{(1 * 0.1% + 5% * 99.9%)} = 1.9627%