The question is concerning a person who "has a positive result", so it seems like the 1/1000 is irrelevant information.
Based on your answer, my initial thinking must not be correct.
If 100 out of 1000 cavemen have an apple, but 5% of the apples are actually a plastic replica of an actual apple.. then only 95 cavemen have apples grown from a tree.
Using your formula, for the above statment to determine how many cavemen have actual apples, I get a value of .65519?
Thank you. The question throws out "prevalence of 1/1000" but then asks about only people with a positive result... a result that is wrong 5% of the time. It doesn't ask about the odds of some random dude having the disease, which is what people are trying to answer. It only asks about people who already have tested positive. And if the test gives a false positive 5% of the time, then 5% of the people who tested positive got the wrong result. People who tested negative aren't part of the actual question. It's more about reading comprehension than maths skills.
If thats an accurate take, then there is a subset of people who are lacking in one life skill, who believe they are more intelligent than the majority because they don't get the same answer..
Now I think I've got to re-examine/reaffirm my beliefs on covid, the 6 million, and lord knows what else..
In that example, you're not calculating how many cavemen have apples. Rather you are calculating the probability, given that you are that a caveman has an apple, that is a real apple rather than a fake one.
So given a prevalence of 0.1 specificity of the test of 0.95 then a PPV around 0.65 seems about right. If your "test" detected an apple, there's about a 65% chance that it's really an apple.
I guess I'm too retarded to wrap my head around 5/100 equating a 65% chance. I knew there was a reason I chose to stay out of professions that puts the lives of others in my hands. :D