In a small town, 10% of the cars registered with the DMV are a model called Sher
ID: 3042235 • Letter: I
Question
In a small town, 10% of the cars registered with the DMV are a model called Sherbrooke. Suppose all cars are equally likely to get involved in a car accident. In a hit-and-run accident, eye witness Dufu claimed that the car that he saw drive away was a Sherbrooke. To check the reliability of his claim, Dufu was asked to identify cars at the location where the accident happened, around the same time of the day and under similar visibility condition. 70% of the time Dufu was able to correctly identify Sherbrookes that drove by and 80% of the time he was able to correctly identify all non-Sherbrookes Suppose it is extremely likely that the car in the accident is local and registered with the DMV. Suppose further that Dufu did not lie.
(a) If we do not consider Dufu’s claim, what is the probability that the hit-and-run car was a Sherbrooke?
(b) What about with Dufu’s claim?
Explanation / Answer
a) P( hit and run car was a Sherbrooke) = Proportion of Sherbrooke cars in town=0.10
b) P( car was sherbrooke) = 0.1* 0.70/[0.1*0.70+0.9*0.20]=0.28
THere is a0.28 probability that the car was a Sherbrooke