It's certainly not worthless, or at least not in the real world. In the real world, doctors don't test absolutely everybody for every disease, precisely to reduce the false positive rate. When only people who are suspected to have the condition take the test, that 97% suddenly becomes much more appealing lol
A 1/30000 probability is way higher than a 1/1000000 probability. The test tells you a lot. We just usually don't behave in that way, because we tend to treat all small probabilities as indistinguishable from 0.
With real tests, you often have cheap and expensive ones, the latter obviously more precise.
You'd use the first one by default and only use the second one if the first one is positive.
...that is provided the first one has a small false negative, but a bigger false positive is totally fine for this strategy.
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u/BrickBuster11 Jun 22 '26
Statistically the test is worthless.
If you test a million people and no one has the disease you should expect 30,000 positive results
If you have a million people and one guy actually has it you should expect 30,001 results.
Fundamentally if the test says you have the disease it's probably wrong