a man is shot in the arm after an encounter with a police officer. the officer claims the man was aiming a gun at her, but no weapon was found. in court, the officer points out that 85 percent of the time, when someone is shot by a police officer, that person was armed. since we know the man was shot by a police officer, she argues, there is an 85 percent probability that he was armed. what error is she making, if any?

Question

15-12-2022
Mathematics

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a man is shot in the arm after an encounter with a police officer. the officer claims the man was aiming a gun at her, but no weapon was found. in court, the officer points out that 85 percent of the time, when someone is shot by a police officer, that person was armed. since we know the man was shot by a police officer, she argues, there is an 85 percent probability that he was armed. what error is she making, if any?

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zaibfatimarizvi zaibfatimarizvi · Answer 1 · 2022-12-21T14:54:55+01:00

Based on the information, the error officer is making is not taking into account the total evidence. (Option D)

The principle of total evidence suggests using all the available observation or evidence when estimating a probability. Hence, to meet total evidence requirement (RTE) not only evidence in favor of a claim but also against it must be considered. The RTE is a basic maxim for non-deductive inference, specifying that evidence must be considered if it has relevance to an inference. The principle of total evidence is tied to inductive inference or reasoning, which is always probabilistic. Total evidence is a tool of decision-making, where the decision is to accept or reject a certain theory/hypothesis on inductive grounds. Hence, logical probability is translated into the (inductive) degree of confirmation of a hypothesis or theory, and that 'logical probability' had to be based on the total evidence available at the time. In the given case, the error the officer is making is not considering the total evidence as she is considering the probability to support her claim but not against it.

Note: The question is incomplete as it is missing options which are a. base rate neglect b. ignoring survivor bias c. heads I win, tails we’re even d. not taking into account the total evidence e. nothing is wrong with her reasoning.

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