A test is positive. What is the chance you actually have the disease? Bayes' theorem combines the base rate (how common the disease is) with the test's sensitivity and false-positive rate: P(D | +) = sens·prior / ( sens·prior + fpr·(1−prior) ). Drag the base rate toward "rare" and watch the posterior collapse - even with a near-perfect test.
Base-rate neglect is the classic error: a "99% accurate" test on a disease only 1% of people have still leaves a positive result far from certain, because the few true positives are swamped by false positives drawn from the large healthy majority. The test quality barely moves the posterior when the base rate is tiny - the base rate dominates. This is a fixed demonstration concept (NOVA's interactive-visual study modality); the per-misconception, per-course generated version is the frontier work that follows.