Bertrand's Box Paradox
Explore the counter-intuitive probability of selecting coins from boxes
The Scenario
Three boxes each contain two coins:
Box 1: Two gold coins
Box 2: Two silver coins
Box 3: One gold and one silver coin
You pick a box at random and draw a Gold coin. What is the probability that the other coin in the box is also Gold?
Theoretical Probability
2/3
Simulated: --%
Why 2/3? Many guess 1/2, but there are 3 ways to draw a gold coin first: Gold #1 from Box 1, Gold #2 from Box 1, or the Gold from Box 3. In 2 of those 3 cases, the remaining coin is Gold.
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