Puzzles
Three boxes, a gold coin, and an answer that isn't 50/50
Three identical boxes each hold two coins: one box holds two gold coins, one holds two silver, and one holds one of each. You pick a box at random and draw one coin without looking at what's left inside it, and it's gold. What's the probability the other coin in that same box is also gold?
Reveal the answer
2/3, not 1/2. Drawing a gold coin is twice as likely to happen from the gold-gold box as from the mixed box, so drawing gold is itself evidence you probably picked the gold-gold box. Joseph Bertrand posed this in 1889 specifically to show how easily probability intuition goes wrong when you ignore how the evidence was generated.
— Joseph Bertrand, Bertrand's box paradox — Calcul des probabilités, 1889