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 pro claims his in no cence and hires you to defend him in court. You hire a scientist to test the witness' ability to distinguish blue and green taxi's under conditions similar to the night of the 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.
Required:
Use this information to perform an analysis where you show that there is reasonable doubt about your clients' guilt

Answer 1

Answer:

the probability the car was actually blue as claimed by the witness is 33.33%. This is a low percentage and thus, there is a reasonable doubt about the guilt of the client.

Step-by-step explanation:

We are given;

P(car is blue) = 1% = 0.01

P(car is green) = 99% = 0.99

P(witness said blue | car is blue) = 99% = 0.99

P(witness said blue | car is green) = 2% = 0.02

We will solve this by using Bayes’ formula for inverting conditional probabilities:

Thus;

P(car is blue | witness said blue) =

[P(witness said blue | car is blue) × P(car is blue)] / [(P(witness said blue | car is blue) × P(car is blue)) + (P(witness said blue | car is green) × P(car is green))]

Plugging in the relevant values gives;

(0.99 × 0.01)/((0.99 × 0.01) + (0.02 × 0.99)) = 0.3333

Thus, the probability the car was actually blue as claimed by the witness is 0.3333 or 33.33%