# Accuracy of HIV test - probability

1. Apr 18, 2007

### DannyCov

Hi everone,

Really stuck on this one, if anyone has any suggestions I would be more than greatful!

Problem:
A HIV test detects at 90% accuracy
It falsly detects people as positive without HIV at 2%
and it is estimated that 50% of the tested patients have HIV

I need to work out the probability that a person does not have HIV and the test is negative?

... but first Im still confused to how to seperate all the conditions, my teacher suggested using contingency tables but the ones I draw up dont make sense to me

Can anyone help? :yuck:

2. Apr 18, 2007

### denverdoc

You know Bayes theorum?

anyhow,
probability that person is HIV negative=1/2
probability of false positive=0.02
therefore (1-.02)=probability of accurate result
product of .5(.98) is what I think you want.

3. Apr 18, 2007

### DannyCov

Ah great thanks thats the way I approached it. The next thing they ask is very vague...
they ask the probability a woman has hiv if the result is positive?
No where else in the question do they say women are any more likely than men so I assume the answer to be another condional probability
P(woman,tumor, PositiveTest)= 0.5 * 0.5 * 90

is this reasonable?

4. Apr 18, 2007

### denverdoc

hmmm, that is vague. I would simply exclude the sex reference and suggest 0.9
as there is no refernce to any notion that false positives are more likely in women than men, so i would interpret the question as a person....