A witness testifying in a hit-and-run case indicates that a green cab hit the plaintiff in the case. You are aware that 85% of the cabs in the city are blue and the other 15% are green. However, the defense attorney conducts an experiment recreating the conditions at the scene, and the witness, when shown green and blue cabs is only able to correctly differentiate them 80% of the time. Assume that prior to the witness' testimony, you would believe there was a 15% probability that a green cab was involved. Thus, what is the probability that in fact a green cab was involved in the accident?
I know that this is the equation I need to use P(G|W) = P(W|G)P(G)/P(W) To get P(W|G) tried multiplying .80 (how many times the wirness can get them right) by .15 (the number of green cars in the city) to get .12 I then multipled that by .15 which is the probability the car was green then divide by .80 the probability the witness was correct. I got .0225 which was not correct.