Any Idea if this is Accurate?

That's not what the scenario said. It didn't say why he went to the doctor, jus that he did. It's very important for analysis to keep track of what is actually going on.

>It didn't say why he went to the doctor

so why did he go get tested?

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The utility here is about extracting accurate information from imperfectly-accurate empirical investigations. Which is all empirical investigations. You can't get around this limit on certainty by ignoring it.

Because it serves the point of the person describing the scenario. If you can't imagine analyzing the situation without an explanation for that, imagine that people are selected for the test by lottery from the general population.

Is this a question on the patient being sick or the reliability of the test?

its accurate and we use it often in game theory and medicine
its also why you see so many different numbers re: corona- the tests are imperfect and it creates a lot of confusion when crafting reliable estimates

that's what i'm getting at. the cunt wasn't a patient till he went to the dr

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Let me clarify: if the tests detects a bacteria in the patient's bloodstream and that bacteria in the quantity of x/mlL is shown to cause sickness then the patient is tested with another tool that relies on another set of probabilistic outcomes and this is why I think that the problem is pretty sloppily presented.

The problem is sloppily presented.
If a doctor knows that 99% of people are sick and 1% of people are healthy, what are the chances that the person that he is talking to is sick...then the answer is 50%.
If we bring words like "tests" and "patient" into the problem then the problem becomes illogical.

Another words: it's the wording of the problem that is a problem not the theorem itself.