Statistical puzzles which must be solved for a good analysis app

Puzzle # 1.
Lets say I have two events that only ever happened once. So think of two flat graphs with one bump each representing, oh, “rock kicked at this moment” and “pain of toe”. Pretend we do not know that the one causes the other. How close must the bumps be in how long a time measured and empty for them to be probably causally related and interesting to a QSer? A book passage would probably be better than an answer.

Only ever happened once? Not enough information as it could just be due to randomness.

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Any correlation COULD be due to randomness but how unlikely must it be to be worth pointing out?

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