Base rate fallacy:

Mathematical Fallacy

Definition	Example
When a probability judgment is made without taking into account known empirical statistics that affect the probability.	The rare disease detection device is 99% accurate, and it detected that I have a rare disease. Therefore I almost certainly do have a rare disease.
Notes
If there are 10 terrorists in a city of 1,000,000, and you have a device on the subway that detects terrorists with a seemingly very high accuracy rate of 99.9%, you are going to experience 100 false positives involving innocent citizens for every terrorist you correctly identify.

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Case Study One

There are sometimes claims of a medical miracles involving patients who were diagnosed with a terminal disease, yet who recovered. To correctly assess the probability of such a claim being true, one needs to compare the number of cases in which there was a correct diagnosis of a terminal illness and supernatural intervention against the number of cases in which there was an incorrect diagnosis of a terminal illness and no supernatural intervention.

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^{Keep in mind that a fallacious argument does not entail an erroneous position.}

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