Accuracy of HIV test - probability

[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 I am still confused to how to separate all the conditions, my teacher suggested using contingency tables but the ones I draw up don't make sense to me

Can anyone help?

 

[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.

 

[DannyCov]

Ah great thanks that's 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?

 

[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...