In a city with one hundred taxis, 1 is blue and 99 are green. A witness observes
ID: 3124479 • Letter: I
Question
In a city with one hundred taxis, 1 is blue and 99 are green. A witness observes a hit-and-run by a taxi at night and recalls that the taxi was blue, so the police arrest the blue taxi driver who was on duty that night. The driver proclaims his innocence, and the driver's attorney hires a scientist to test the witness’ ability to distinguish blue and green taxis under conditions similar to the night of accident. The data suggests that the witness sees blue cars as blue 99% of the time and green cars as blue 2% of the time. What is the probability that the car observed by the witness was green?Explanation / Answer
Let
B, G = the actual color was blue, green respectively
b, g = the observed color was blue, green, respectively
As
P(b) = P(B) P(b|B) + P(G) P(b|G) = (1/100)*0.99 + (99/100)*0.02 = 0.0297
Hence,
P(G|b) = P(G) P(b|G) / P(b) = (99/100)*(0.02)/0.0297 = 0.666666667 [ANSWER]