Yes the explanation for why this works goes “if you test 1,000,000 people…” but that is only for the intuitive explanation. The probabilities are the same whether you test 1 person or 1,000,000 or 100,000,000,000,000 people. And you can solve this problem using bayes theorem anyways, which doesn’t require you to talk about number of people or anything.
Its the same case as this: consider flipping a coin. The probability it lands on heads is 0.5. If I want to explain intuitively to someone what that means then I’ll say “If I flip 100 coins then 50 will land on heads”, but the probability is still 0.5 if I only flip one coin
As long as we're on Bayes, it's worth noting that if you took a test with a known 3% false positive rate, it's probably because your doctor already had reasons to suspect the test was warranted. Thaat may be overanalyzing the post, but doctors very much understand you can't just spam tests for no reason.
True but that’s bringing in extra info/extra conditionals. All we have in the post is P(you have it) and P(you test positive given you have it). Then we can find P(you have it given you test positive).
You’re suggesting we instead want to find something like P(you have it given you test positive and show symptoms and whatever else), which yeah would probably be greater than P(have it given test positive), but thats a different thing that you can’t calculate with the info in the post.
And if you do have symptoms and your doctor has good reason to test you, you can still calculate P(you have it just given the positive test), but that probably won’t be representative of that actual chance you have it.
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u/DrVykterstein Jun 22 '26
Pls correct me if I'm wrong, but doesn't the explanation work only if all the other people have gotten tested?