A witness to a hit-and-run incident reports that he saw a blue taxi hit a pedest

Question

A witness to a hit-and-run incident reports that he saw a blue taxi hit a pedestrian. The
town only has blue and green taxis, and the witness is 90 percent reliable: that is, if he
sees a green taxi he has a 0.9 probability of reporting green (0.1 of reporting blue), and if
he sees a blue taxi he has a 0.9 probability of reporting blue (0.1 of reporting green). We
know that the town has 80 percent green taxis, 20 percent blue. What is the probability
that a blue taxi was actually involved in the accident?

Explanation / Answer

Probablity of reporting a blue taxi = 0.2x0.9 + 0.8x0.1

= 0.26

therefore probablity of blue taxi to be involved is 0.9x0.2/0.26

= 0.69

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