paradox · traps · doors
Bertrand's box paradox
A gold coin is showing. How often is the other side gold too?
A gold coin is showing. How often is the other side gold too?
Three boxes. One coin is drawn. Only a gold coin on the table counts.
Lock a share, then draw.
—This other coin
—Draws where the other coin was gold
—Long-run share for this rule
The boxes are gold-gold, gold-silver, and silver-silver. Each box is equally likely, and so is each coin inside the box you picked.
A gold coin on the table is one of three gold faces. Two of those faces have gold on the other side.
Counting faces, the other coin is gold about 2 in 3 draws. Dropping the silver box and treating the other two boxes as equal lands near 1 in 2.