Abstract
In real life, we use math all the time without realizing it, whenever a hard decision is necessary. You leave a piece of cake on the table while you go do an errand, and when you come back it has disappeared. Should you call the police to report an intruder? You put together all the facts you can dredge up: the probability that unfamiliar people are nearby, that the door was safely locked, that the people nearby are really hungry, that someone in your family would take it without telling you, that you might have forgotten that you put it in the refrigerator, that the dog is in the next room, that the dog is tall and clever enough to get onto the table, etc. Then you put all these probabilities together and decide how they compare to the probability that it was a cake thief. If you wind up deciding that the not-intruder possibility is at least 40 times more likely than the intruder possibility, you relax. You have just crudely rejected the intruder hypothesis with a precision about the same as the conventional scientific confidence level.
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