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wasoxygen  ·  3637 days ago  ·  link  ·    ·  parent  ·  post: For everyone in the book exchange: The Necessity of Marginalia

Based on the evidence given, we can calculate a probability of 41% that the cab was blue. This witness is pretty reliable, but blue cabs are rare and it is more likely that the witness is mistaken than that the cab was really blue.

My approach was to imagine 100 hit-and-run accidents. In 85 of them, the cab will be green, in 15 blue.

Of the 85 green accidents, the witness will correctly see 67 green cabs (eighty percent accuracy) and mistakenly see 17 blue cabs.

Of the 15 blue accidents, the witness will correctly see 12 blue cabs and mistakenly see 3 blue cabs.

We are told that the witness saw blue. So we are considering one of the 17 mistaken identifications or 12 correct identifications, a total of 29 cases. The witness is correct (and the cab is really blue) in 12 out of 29 cases, about 41%.