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Conjunction Fallacy

It seems to me like a fine way to avoid this fallacy is to always, as a habit, disassemble statements into atomic statements and evaluate the probability of those. Even if you don't use numbers and any of the rules of probability, just the act of disassembling a statement should make the fallacy obvious and hence easier to avoid.

I think this fallacy could have severe consequences for criminal detectives. They spend a lot of time trying to understand the criminals, and create possible scenarios. It's not good if a detective finds a scenario more plausible the more detailed he imagines it.