# Conditional Probability

1. Apr 29, 2013

### Darth Frodo

1. The problem statement, all variables and given/known data

In 1988, the state of Illinois required HIV testing for a couple to obtain a marriage
license. The HIV testing at the time consisted of two separate tests, the ELISA
test and the Western Blot test. The Elisa test was signi cantly less expensive. A
person who is HIV positive would test positive under the ELISA test 95% of the
time. A person who is HIV negative would test positive under the ELISA test 99%
of the time. In 1988, it was estimated that the percentage of people applying
for a marriage license that were actually HIV positive was 1%.

If someone test positive on the ELISHA test, then that person is given the West-
ern Blot test. A person who is HIV positive will test positive on the Western
Blot test 99% of the time, while a person who is HIV negative will test positive
on the Western Blot test 5% of the time. What is the conditional probability that someone is HIV positive given that the person tests positive on both the Western Blot and the ELISHA test?

3. The attempt at a solution

Basically I drew a tree diagram to figure this out, but it seems very low. I would appreciate it if someone could tell me where I'm going wrong.

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2. Apr 29, 2013

### Staff: Mentor

I think this should be "negative" (or 1% instead of 99%), otherwise the test would be very strange.
While this should change your result to a larger value, small probabilities to have some rare disease are not uncommon in medical tests in general.

3. Apr 29, 2013

### Darth Frodo

Yes, I think you're right. I completely misread the question. Although, I think my confusion is rather valid.