defender's fallacy

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A mis-statement of a probability as a result of a misunderstanding of conditional probability. See also prosecutor's fallacy. As an example, suppose that a blood type possessed by only 1% of the population is found at a crime scene. The accused has blood of this type. The defender argues that, since the population size is one million, there are 10 000 with this blood type and therefore the probability that it is the accused who is guilty is 1 in 10 000.

For a randomly chosen person, let A be the event ‘person chosen has blood of this type’ and let B be the event ‘person chosen is guilty’. The figure quoted by the defender is P(B|A), whereas the probability of interest is P(accused is guilty).

Subjects: Probability and Statistics.

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