Should you believe the witness of crime eyes? (Bayes formula)
What if the probability of correct object identification is less than 100%
I have taken the problem statement from a matematician Boris Trushin’s youtube channel → https://www.youtube.com/watch?v=UfeAMEav_Dc (the video in Russian, subtitles n/a, but the language of numbers is international)
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The crime
Let’s imagine you are a detective in a small town. Last night there was a traffic accident where a taxi hit a pedestrian to death and drove away. There is one witness of the crime. You have discussed the accident with the witness, and he claimed that the accident was in the dark, at some distance away from him. Also, he didn’t see the taxi plate, but he was sure that the taxi was yellow.
You know there are only two taxi companies in the town. The “Yellow” company’s cars are yellow, and its share is 15% of all taxi cars. The “White” company’s cars are white, and its share is 85% of all taxi cars. If the witness said the car was yellow, it is much less work to search for the vehicle, isn’t it?
Please take some moments to comprehend the situation.
