Full Idea
In the 'cab problem' (what colour was the cab in the accident?) most people estimate an 80% probability of it being a blue cab, but Bayes' Theorem calculates the probability at 41%, suggesting people put too much faith in eyewitness testimony.
Clarification
Bayes' Theorem is an equation for calculating probability, given a certain observation
Gist of Idea
People are wildly inaccurate in estimating probabilities about an observed event
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
For details of the 'cab problem', see Lowe p.200. My suspicion is that people get into a tangle when confronted with numbers in a theoretical situation, but are much better at it when faced with a real life problem, like 'who ate my chocolate?'