General
The Gold Ball Box Riddle Almost Everyone Gets Wrong
Bertrand box paradox: three identical boxes — one holds two gold balls (GG), one holds a gold and a silver (GS), and one holds two silver balls (SS). You open a random box and draw a random ball — it is gold. What is the probability that the other ball in the same box is also gold?
People also ask
What is the answer to the Bertrand box paradox riddle?
The probability that the other ball is also gold is 2/3, not 1/2.
Why isn't the answer 1/2?
There are three equally likely gold balls you could have drawn, and two of them live in the gold-gold box. So in 2 out of 3 cases the partner ball is also gold, giving 2/3.
What is the Bertrand box paradox?
It's a classic conditional-probability puzzle by Joseph Bertrand showing that intuition (1/2) often misleads us; the correct answer is 2/3.