Full Idea
'Base rate neglect' (attending to the witness or evidence, and ignoring background information) is responsible for doctors exaggerating the significance of positive results in diagnosis of relatively rare medical conditions.
Gist of Idea
'Base rate neglect' makes people favour the evidence over its background
Source
E.J. Lowe (Introduction to the Philosophy of Mind [2000], Ch. 8)
Book Reference
Lowe,E.J.: 'Introduction to the Philosophy of Mind' [CUP 2000], p.201
A Reaction
This seems to be one of the clearest cases where people's behaviour is irrational, though I suspect that people are much more rational about things if the case is simple and non-numerical. However, people are very credulous about wonderful events.