You are standing before a huge barrel of apples. You can’t see the apples, but you can reach in and pick them out. Most are delicious, but a very small number of them are rotten—just about one in 12,000, your friend assures you. You reach in blindly and miraculously pick out a rotten apple. You reach in again and withdraw a whole heaping bushel of apples, maybe 50 in all. Most are good, but when you look closely you see them: one, two, three, four more rotten apples. One rotten apple is an amazing coincidence. Five means your barrel has lots of rotting apples in it and your friend was lying to you.

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