The probability of a conjunction between two events (A and B) can't be more likely than a single one of the events (A) or (B).

University of Michigan - Ann Arbor

The mind tends to ignore base rates (even if informed) and focuses on the most recently discovered evidence. Generally underweighted or neglected when specific casee information is available

base rate neglect (fallacy)

Goldstein, E. B. (2014). Cognitive psychology: Connecting mind, research and everyday experience. Nelson Education.


Cognitive psychology: Connecting mind, research and everyday experience

A cab was involved in a hit and run. There are two cab companies, red and blue. What is the probability the cab involved in the accident is blue?

Respondents neglect the base rate (most common answer = 80%) when the story is phrased:

- 85% of cabs are green and 15% are blue

- A witness identified the cab as blue. During the cross examination, the witness correctly identified one of the two colors 80% of the time and failed 20%

Respondents give answers close to the Bayes rate (41%) when the story is phrased:

- The two companies operate the same number of cabs, but green cabs are involved in 85% of accidents

- A witness identified the cab as blue. During the cross examination, the witness correctly identified one of the two colors 80% of the time and failed 20%

Mathematically the problems are exactly the same, but in the second explanation of the story, a psychological causal link between green cabs and accidents is established because of the wording.

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