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> The doctors who perform these tests are trained to understand this type of stuff. They're not just blindly accepting any single test result

They're "trained to understand this type of stuff" in the sense that it will get a mention in medical school. Overwhelmingly, they aren't "trained to understand this type of stuff" in the sense that if you pose them a simple problem of this type, they'll be able to calculate the answers.

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From An Intuitive Explanation of Bayes’ Theorem [0]:

> Next, suppose I told you that most doctors get the same wrong answer on this problem – usually, only around 15% of doctors get it right. (“Really? 15%? Is that a real number, or an urban legend based on an Internet poll?” It’s a real number. See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. It’s a surprising result which is easy to replicate, so it’s been extensively replicated.)

[0] https://www.yudkowsky.net/rational/bayes

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