In a city with one hundred taxis 1 is blue and 99 are green

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 hires you to defend him in court. You hire 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. Write a speech for the jury to give them reasonable doubt about your clients guilt. Your speech need not be longer than the statement of this question. Keep in mind that most jurors have not taken this course, so an illustrative table may be easier for them to understand than fancy formulas.

Solution

the total cars are 100 out of which 1 is blue and 99 are green so the probability of blue car to be on road = 1/100 = 0.01 while the probability of green car to be on road is 99/100 = 0.99. now thw witness according to the data has 99% cahnce to see blue as blue but also 1% he does not recognise the correct color. so 1% of 0.01 = 0.0001 is the chance that he the witness is correctly recognising the color of the car on that spot also the witness see 2% times green as something else

so 2% of 0.99 = 0.0198 chnace he get the wrong color of the green car. adding both the situation we get 0.0200 chances that the witness is wrong which is not beyond doubt neither 100% sure about the guilt of my client.