A cab was involved in a hit and run accident at night. A witness identified the guilty cab as blue. Agreed data:
- Two cab companies, the Green and the Blue, operate in the city.
- 85% of the cabs in the city are green; 15% are blue
- In a scientific test under the same conditions as existed on the night of the accident the witness was found to identify correctly each of the two colours 80% of the time.
What is the probability that the cab involved in the accident was green rather than blue and that the witness was wrong?
Those of you who are mathematic/scientific by background will already be well on the way to working out the correct answer and can probably do it quite quickly. (Your maths has honed your intuition as it were.) For those who are not, and who couldn't imagine how to begin, let me know, intuitively, if you would trust this witness and use his/her evidence to sway a conviction for say, manslaughter, or leaving the scene of an accident, both of which carry custodial sentences.