Tukuk-OSA screening test is a machine that fires when things are wrong — and sometimes when they are not. Take a disease affecting 1 in 10,000 and a genuinely excellent test: it flags 99% of true cases and false-alarms on 1% of healthy people. Run it on 100,000 people. Expect about 10 sick and 99,990 healthy. The sick mostly light up: ~10 true positives. But the healthy produce ~1,000 false positives — the base is so huge that 1% of it dwarfs the disease. Now you have about 1,010 positives and only ten of them are real: a positive result means roughly 1% chance of disease, not 99%. This is the base-rate fallacy in one arithmetic block, and it is why any positive screening test demands a confirmatory test, ideally with a different mechanism.
The same arithmetic polices your whole information diet. “This symptom matches a rare condition” — the common conditions are common for a reason; a match to a rare profile is far more likely the thousand-to-one false positive than the disease. “This stock tip matches patterns that worked twice before” — the base rate of tips beating the market is near zero, so the pattern evidence needs a huge likelihood ratio to move the prior at all. Bayes’ rule is not a formula to memorise; it is the discipline of letting the rarity of a thing discount the strength of signals about it.
The honest flip side: the base-rate reasoning cuts both ways. When a test is extremely specific and the population enriched (a specialist referring high-risk patients), positives genuinely mean something. The skill is never “trust the test” or “distrust the test” but knowing which population you are in — your prior is a number, and you can update it the same way you update everything else.