If any order is equally likely to come from any of twenty traders, a buy order puts the posterior at 21/40 and forces an honest ask five cents above a mid of zero, so the spread is 2/N whatever the crowd's size. Each of the nineteen uninformed traders then loses exactly five cents a trade, which sums to the insider's 95 cents because (N-1)/N and 1 - 1/N are the same number. Volume falling is a comparative static on top of that spread rather than a theorem of the model, and naming the insider would have repaired the market instead of breaking it, since a known informed trader can simply be refused.
Coins have no memory, which is true, and nobody said this coin is fair, which is the whole problem. A fair coin explains the run with probability two to the minus one hundred while a two-headed coin explains it every time. The article locates the threshold exactly and reconciles the answer with the companion piece on ten heads, which asks a different question about a different setup.
Deux portes restantes ne font pas deux portes égales : votre premier choix est resté figé à 1/3, et les 2/3 restants se sont entassés sur la seule porte encore fermée. Le nombre ne dit rien des portes, il dit tout du présentateur. Laissez-le ouvrir au hasard, montrez la même chèvre, et changer ne vaut plus que 1/2.
Six slots in a ring, two of them marked side by side. You land on a blank one and get one move: step forward, or draw a fresh slot at random. Both look like two in six. Stepping is one in four, drawing again is one in three, and the whole gap comes from the fact that the two marks are touching. Pull them apart and the advice reverses.
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.