A counter-intuitive probability puzzle involving three boxes.
Simulation
Click "Pick Box" to randomly select a box and draw one coin. If it's Gold, you can guess the other side.
Results
Long Term Probability (Given 1st is Gold)
2/3 (66.6%)
Expected "Other is Gold"
Trials (Seen Gold)0
Observed Prob.0.0%
Found Gold Again (GG)0
Found Silver (GS)0
About this calculator
Overview
There are 3 boxes: Box 1 (2 Gold coins), Box 2 (1 Gold, 1 Silver), Box 3 (2 Silver coins). You pick a box at random, and pick a coin at random. It's Gold. What is the probability the other coin is also Gold?
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Pro Tips
Try running the simulation many times to see the probability converge to 66.6%.
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Fun Facts
"Most people intuitively guess 1/2, thinking it's either Box 1 (GG) or Box 2 (GS)."
"The correct answer is 2/3, because there are 3 Gold coins in total that you could have picked, and 2 of them belong to Box 1."
