A screening test for a rare condition comes back positive, and you first click a probability bar to record your guess of how likely the condition really is. The reveal shows Bayes' rule as a walk on the log-odds ruler: a 1-in-1,000 prior starts at about minus 6.9 points, a 99-percent-accurate test adds ln(99), about plus 4.6 points, landing at minus 2.3, which the sigmoid turns into roughly 9 percent. Sliders for rarity, sensitivity, and false-alarm rate update the walk live, and presets show a coin-flip prior giving 99 percent, a 1-in-100,000 prior giving about 0.1 percent, and taking the test twice giving about 91 percent.

The test says yes. Bayes says wait.

A screening test for a rare condition. Set the scene below, then commit to a guess — the answer is one addition on the straight ruler: prior + evidence.

Bayes’ rule, on the straight ruler, is one addition: where you start (the prior) plus what the test is worth (the evidence). A 99%-accurate test is +4.6 points — but 1-in-1,000 starts you 6.9 points below zero. The “paradox” was never about the test; it was about forgetting where the walk starts.