A witness testifies that the taxicab that struck and injured Smith in a dark alley was green. On investigation, the attorney for Green Taxi Company discovers that the witness identifies the correct colour of a taxi in a dark alley 80 per cent of the time. There are two taxi companies in town, Green and Blue. Green operates 15 per cent of all local taxis. The law says that the Green Taxi Company is liable for Smith's injuries if and only if the probability that it caused them is greater than 0.5. Is Green liable? Explain.

WITH DIAGRAMS IF possible AND GOOD explanation !