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Your examples are nice theoretical illustrations of the effects, on statistical estimates, of failing to take ‘base rates’ into account. However, it seems to me that it w/d be impossible to arrive at rates which were sufficiently relevant/accurate to be applicable in practice. Consider the covid example: It w/d not be feasible to derive a natural frequency (“from observing cases that have been representatively sampled from a population”; or otherwise) that could realistically be applied to a self-selected individual undertaking a RAT test (because: symptoms, close contacts, occupation, location etc). Analogous issues (eg: age, family history, genes, race etc) would likely apply to the breast cancer example.

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