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Bertrand's box paradox
A problem, similar to the Monty Hall problem, which was published by the French mathematician Joseph Bertrand (1822-1900) in his 1889 text Calcul des Probabitités. Suppose there are three desks, each with two drawers. One desk contains a gold medal in each drawer, one contains a silver medal in each drawer, and one contains one of each, but you don't know which desk is which. The question is this: If you open a drawer and find a gold medal, what are the chances that the other drawer in that desk also contains gold? This comes down, then, to figuring out the probability that you've picked the gold-gold desk instead of the gold-silver desk. Many people quickly jump to the conclusion that there are two possibilities, and since the selection was random, it must be 50-50. But this is wrong. Think of the initial selection as picking from among six drawers:
| before | ||
|---|---|---|
| S | S | G |
| S | G | G |
| 1 | 2 | 3 |
| after | ||
|---|---|---|
| G | G | |
| G | ||
| 1 | 2 | 3 |
So, we have it narrowed down to three drawers, with an equal probability of each one being the one that was picked. One of the drawers is in desk 2, so there's a 1/3 chance that desk 2 was picked. Two of the drawers are in desk 3, so there are two 1/3 chances (i.e. a 2/3 chance) that desk 3 was picked.
Related category
• PARADOXES
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