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A taxi was involved in a hit-and-run accident at night. Two taxi companies, the green and the blue, operate in the city. 85% percent of the taxis are green and 15% are blue. A witness identified the taxi as blue.The witness identifies the correct color 80% of the time and fails 20% of the time. What is the probability that the taxi was blue?

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  • $\begingroup$ Since your answer is wrong, perhaps you're not the best judge of where the post belongs. $\endgroup$ – BobRodes May 29 '16 at 18:20
  • $\begingroup$ What about mine? $\endgroup$ – ev3commander May 29 '16 at 18:21
  • $\begingroup$ @BobRodes, my mistake. I didn't realise there was more to it. $\endgroup$ – Beastly Gerbil May 29 '16 at 18:23
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    $\begingroup$ As someone who did get the correct answer (before looking at the submitted ones), I’m not at all sure why this is in puzzling rather than just math.stackexchange. It seems like a straightforward probability exercise dressed up in a word problem, and with several important assumptions (e.g. that the witness’s chance of correctness is independent of the colour of the taxi) omitted. There’s no particular imagination or insight involved. $\endgroup$ – Peter LeFanu Lumsdaine May 29 '16 at 18:32
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    $\begingroup$ @BobRodes it is completely normal to make mistakes when you join a new forum, everyone does. But when other, more experienced users tell you you are wrong, you don't need to become hostile. This indeed is place for having fun, but in order to improve the experience, we try to stick to some posting rules. $\endgroup$ – Puzzle Prime May 30 '16 at 1:25
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12/29

Because

the chance of it being blue and the witness being correct is 0.12. Or he saw blUE but it was green, which is a 0.17 chance. 0.12/(0.12+0.17)= 12/29.

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  • $\begingroup$ what do you mean "blUE but it was green". Could you explain that? $\endgroup$ – Beastly Gerbil May 29 '16 at 18:22
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    $\begingroup$ He's referring to the chances that a blue car was incorrectly identified as green, which your answer doesn't take into account. $\endgroup$ – BobRodes May 29 '16 at 18:23
  • $\begingroup$ The witness incorrectly identified a green taxi as blue = 85%*20% $\endgroup$ – ev3commander May 29 '16 at 18:23
  • $\begingroup$ @bob nope, the opposite :p $\endgroup$ – ev3commander May 29 '16 at 18:25
  • $\begingroup$ Well done! I'll have to come up with something tougher, although when I last tried a year ago, several people marked my problem as a dup of another problem which actually had a different answer. $\endgroup$ – BobRodes May 29 '16 at 18:25

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