Question

Two companies compete for the taxi market in Someville. 14 percent of the taxicabs belong to the Blue company, and the rest to the Yellow company. One night there was a hit and run accident, and a witness reported that she saw a Blue cab speeding a way from the scene. Further testing showed that the witness is 86 percent accurate in identifying the color of the cab under similar distance and lighting conditions. What is the probability that the cab involved in the accident actually is Blue?

Enter answer as decimal probability between 0 and 1, accurate to 5 decimal places.

Answer 1

Lets assume there are 100 cabs in the city:
blue = 14, yellow=86
Total no of blue cabs identified correctly = 14 * 0.86 = 12.04

Witness is incorrect 14% of the times identifying the cab as green.

Total no of yellow cabs identified incorrectly = 86 * 0.14 = 12.04

Total number of cabs identified by the witness will be 12.04+12.04=24.08

Hence the probability of identifying blue cab correctly is = 12.04/24.08=50%

Hence there is 50% probability that cab involved is actually blue