A small town has 100 cabs. 70 cabs are blue (Blue Cab Company) and 30 cabs are g

Question

A small town has 100 cabs. 70 cabs are blue (Blue Cab Company) and 30 cabs are green (Green Cab Company). There is a hit-and-run accident at night (pedestrian injury, not fatality) and an eyewitness present at the scene of the accident claims it was a green cab that struck the pedestrian. No criminal charges tire laid, but the injured party does bring a civil lawsuit against the Green Cab Company to recover costs associated with hospitalization and lost wages. The witness is called to testify ('I saw a green cab strike the pedestrian'). The witness is also subjected to a vision test and it is found that under conditions similar to those on the night of the accident, the witness can correctly identify a cab from other types of vehicles and the witness can correctly distinguish the colour of the cab (blue or green) X% of the time. The judge in the case will find in favour of the plaintiff if the beliefs of the judge assign a probability of greater than 50% to a green cab being involved in the hit-and-run. If X% = 100% (the witness always identifies the correct colour of the cab), how should the judge rule in this case? If X% = 75% (the witness correctly identifies the colour of the cab 75% of the time), how should the judge rule in this case? Suppose that evidence is presented that show' that on the night in question there were only 60 of the 70 blue cabs in service and 25 of the 30 green cabs in service. Would this lead to a change in the ruling of the judge (X% = 75%).

Explanation / Answer

a)Jugdement will be against Plaintiff.

Reason probability is less than 50%

(0.3*1 = 0.3)

..

b)Judement will be against plaintiff

Reason probability is less than 50%

(0.3*0.75 = 0.225)

..

c)Answer will be same as part-b.

Reason :-

Probability that it will be a green car = 25/(25+60) = 0.30

..

For part a & b Probablity that it will be a green car = 30/(30+70) =0.3

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