There are two cab companies operating. The Blue Cab Companyoperates only blue ca
ID: 2916110 • Letter: T
Question
There are two cab companies operating. The Blue Cab Companyoperates only
blue cabs, and the Green Cab Company operates only greencabs. Exactly 85% of the cabs in
Barnsdall are blue, and 15% are green. A cab was involved ina hit-and-run accident at night.
An honest eyewitness, Wilbur, identified the cab as a greencab. It was found that Wilbur could
correctly identify the color of cabs at night 80% of thetime. Given that Wilbur said that he saw
a green cab, what’s the probability that the actual cabinvolved in the hit-and-run was from the
Green Cab Company?
Explanation / Answer
Define P(G) = probability of car being a green cab, P(B) =probability of a car being a blue cab, P(SG) = probability ofseeing a green cab (correctly or incorrectly) P(G) = 0.15 P(B) = 0.85 P(SG|G) = 0.8 P(SG|B) = 1 - 0.8 = 0.2 We want to find P(G|SG). P(SG ^ G) = P(SG|G)*P(G) = 0.8*0.15 = 0.12 P(SG) = P(SG|G)*P(G) + P(SG|B)*P(B) = 0.8*0.15 + 0.2*0.85 =0.29 P(G|SG) = P(SG ^ G)/P(SG) = 0.12/0.29 = 0.414 The probability is 0.414.