Ok, and would your answer be different if I told you the false positive rate on the test was 30%?
So....
There's a 30% chance I've been misdiagnosed as having a disease that will kill me, for sure, in a week.
I can take drug A, which will cure me for sure, but then has a 20% chance of killing me with side effects, OR
I can take drug B, which will cure me 70% of the time, with no side effects.
Case 1: I have the deadly disease (70% chance)
Drug A: 20% chance of death x 70% = 14% Drug B: 30% chance of death x 70% = 21%
Case 2: False positive, I'm fine (30% chance)
Drug A: 20% chance of death x 30% = 6% Drug B: No chance of death
I have a 20% chance of dying with Drug A, and a 21% chance of dying with Drug B. Close to a wash, but I'm still in the Drug A camp.
“The trick is in what one emphasizes. We either make ourselves miserable, or we make ourselves happy. The amount of work is the same.” Carlos Castaneda