You draw a gold coin from a box. What are the odds the other coin is gold too?
There are three boxes: one holding two gold coins, one holding two silver coins, and one holding one of each. You pick a box at random and draw one coin from it, which turns out to be gold. What is the probability that the other coin in that same box is also gold?
Reveal the answer
2/3, not 1/2 as most people guess. There are three gold coins you could have drawn in total: two of them sit in the all-gold box and guarantee a gold partner, while only one sits in the mixed box and doesn't. Mathematician Joseph Bertrand posed this in 1889 to show how easily people misjudge conditional probability; it's a direct ancestor of the Monty Hall problem.