The five treasure chests

Question

Five identical chests sit on a table, and exactly one holds gold. You point to one chest and leave it closed. The keeper, who knows where the gold is, then opens three of the remaining four chests, all of them empty. One other chest is still closed.

If you switch your choice to that last closed chest, what is your probability of winning the gold?

Accepted Answer

Your first pick is correct with probability 	frac{1}{5} and wrong with probability 	frac{4}{5}. Those are locked in before the keeper does anything. Now think about what the keeper's move tells you. The keeper never opens the gold chest, only empties. - If your first pick was already the gold chest (probability 	frac{1}{5}), the gold is in your hand, and the last closed chest is empty. Switching loses. - If your first pick was wrong (probability 	frac{4}{5}), the gold is among the other four chests. The keeper opens three of those four, all empty, so the one closed chest he leaves behind …

The five treasure chests

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