You might wonder why there's a requirement of 5σ (standard deviations away from the expected value) for a discovery--you don't require that sort of extreme deviation in ordinary life, right? If you flip a coin 10 times and it comes up heads every time, you wonder if the coin is doctored; that's a 1 in a thousand chance, but less than 5σ. But if you're flipping a thousand coins at once and you want to know if one is doctored, you have to flip for a long time. After all, with a thousand choices, you expect at least one to show up all heads.
It's the same way with looking at the sky. You don't know where to look for a signal, so it has to be a pretty dramatic one to rise above random fluctuations. (My advisor used to say "Prior knowledge is worth 3σ.")
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