The base rate fallacy is so misleading in this example because there are many more non-terrorists than terrorists.

This is called the base rate fallacy.

For other errors in conditional probability, see the Monty Hall problem and the base rate fallacy.

The base rate fallacy explained visually (Video)

Someone making the 'base rate fallacy' would infer that there is a 99% chance that the detected person is a terrorist.

An extreme example of the base rate fallacy is to conclude that a male person is pregnant just because he tests positive in a pregnancy test.

As can be seen, the base rate P(H) is ignored in this equation, leading to the base rate fallacy.

(Base rate fallacy)

Mathematician Keith Devlin provides an illustration of the risks of committing, and the challenges of avoiding, the base rate fallacy.

The Base rate fallacy in medicine, or the Prosecutor's fallacy in legal reasoning, consists of making the erroneous assumption that .

Similarly in medical diagnosis and legal reasoning, the same methods are being used, although there have been many examples of errors, especially caused by the base rate fallacy and the prosecutor's fallacy.

In many real-world situations, though, particularly problems like detecting criminals in a largely law-abiding population, the small proportion of targets in the large population makes the base rate fallacy very applicable.

Physicians have difficulty in estimated risks of diseases; frequently erring towards overestimation, perhaps due to cognitive biases such as base rate fallacy in which the risk of an adverse outcome is exaggerated.

However, it has been argued that many standard tests of reasoning, such as those on the conjunction fallacy, on the Wason selection task, or the base rate fallacy suffer from methodological and conceptual problems.

Not adjusting to the scarcity of the condition in the new population, and concluding that a positive test result probably indicates a positive subject, even though population incidence is below the false positive rate is a "base rate fallacy".

Richard Nisbett has argued that some attributional biases like the fundamental attribution error are instances of the base rate fallacy: people underutilize "consensus information" (the "base rate") about how others behaved in similar situations and instead prefer simpler dispositional attributions.

This file drawer problem results in the distribution of effect sizes that are biased, skewed or completely cut off, creating a serious base rate fallacy, in which the significance of the published studies is overestimated, as other studies were either not submitted for publication or were rejected.