A driver responsible for a car accident disappears after the accident. After investigating the case, police believe
Question:
A driver responsible for a car accident disappears after the accident. After investigating the case, police believe with 70% probability that the accident was caused by a car with plate number XYZ 1867. At this point, an eye witness appears and tells the police that he is certain that the last digit in the number plate of the car was 7, but he did not see or remember any other digits or letters from the plate. Using this piece of information, what is now the probability that the driver of the car with plate number XYZ 1867 caused the accident?
Suppose alternatively the eye witness says he is only 90% certain that the last digit of the plate is a 7; what would be the probability that the accident was caused by a car with plate number XYZ 1867 in this case?
In both cases, assume that every combination of three letters and four digits has the same probability of appearing in a plate number.
(Hint: Use Bayes’ theorem.)
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