Une maladie que porte une personne sur deux cents, et un test sans le moindre faux négatif. La réponse réflexe à un résultat positif dépasse les quatre-vingt-dix pour cent, et elle se trompe d'un facteur dix. Une foule de mille personnes montre pourquoi avant que l'algèbre ne s'en mêle, et Bayes fixe la valeur exacte à 100/1493.
Aussi posé sous le nom debase rate fallacy · false positive paradox · medical test paradox
Lire l'explication complète — Un test qui ne rate jamais, un résultat positif, et 6,7 %
Draw one coin from a thousand, flip ten heads, and the chance it is the two-headed one is 0.5062. Both reflex answers miss, in opposite directions: ninety-nine percent ignores the bag, one in a thousand ignores the flips. Counting patterns gets the exact figure with no Bayes notation at all, and the reason it lands on a coin flip is that 2^10 happens to sit next to the size of the bag.
Fifty white marbles, fifty black, two jars, and a fair coin choosing which jar gets drawn from. The even split gives exactly one half, and so does every other split where the jars are the same size. Isolating a single white marble reaches 74/99, an exchange argument proves nothing beats it, and three quarters turns out to be a ceiling no arrangement ever touches.
Drop chips at random into dough, cut it into a hundred cookies, and ask how many chips guarantee no bare cookie nine times out of ten. Five hundred chips, five per cookie on average, works about half the time. Inclusion-exclusion pins the answer at 683, a closed form you can solve on a whiteboard agrees, and the coupon collector's mean of 518.7 is the sophisticated wrong answer.