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OFF TOPIC -- A question of logic

Posted By: joe freedman
Date: Saturday, 2 May 2015, at 4:12 a.m.

"Thinking Fast and Slow," an interesting book by the Nobel laureate Daniel Kahneman, contains the following problem: A taxicab is involved in an accident late at night. In the city at issue, 85% of the cabs are green, and 15% are blue. A witness identified the cab as blue. It has been determined that, under the conditions that existed that night, the witness is 80% accurate in distinguishing between the two colors.

Now, assuming the witness is not lying, what is the probability that the cab is blue?

I would have said 80%, because the witness said it was blue and the witness is right 80% of the time. Why should the "base rate," or the percentage of blue and green cabs in the city be relevant? Of course, if the fleet was 100% green, the witness' opinion would have no relevance. But if there's at least 1 blue cab in the fleet, why isn't the witness' 80% accuracy determinative?

Kahneman says the Bayesian answer is 41%. My guess is that I am wrong on this, but can anyone explain?

Messages In This Thread

• OFF TOPIC -- A question of logic
  joe freedman -- Saturday, 2 May 2015, at 4:12 a.m.
  • OFF TOPIC -- A question of logic
    Jake Jacobs -- Saturday, 2 May 2015, at 5:11 a.m.
    • OFF TOPIC -- A question of logic
      Taper_Mike -- Saturday, 2 May 2015, at 7:31 a.m.
      • +1 *NM*
        Jim Stutz -- Sunday, 3 May 2015, at 3:35 a.m.
    • OFF TOPIC -- A question of logic
      Fatboy -- Sunday, 3 May 2015, at 7:06 p.m.
  • OFF TOPIC -- A question of logic
    Art Grater -- Saturday, 2 May 2015, at 6:40 a.m.
  • OFF TOPIC -- A question of logic
    rambiz -- Saturday, 2 May 2015, at 9:50 a.m.
    • OFF TOPIC -- A question of logic
      Mike Clapsadle -- Saturday, 2 May 2015, at 11:29 a.m.
      • OFF TOPIC -- A question of logic
        Timothy Chow -- Saturday, 2 May 2015, at 6:17 p.m.
        • OFF TOPIC -- A question of logic
          Bob Koca -- Saturday, 2 May 2015, at 6:26 p.m.
        • OFF TOPIC -- A question of logic
          Havard Raddum -- Saturday, 2 May 2015, at 6:28 p.m.
          • OFF TOPIC -- A question of logic
            Timothy Chow -- Saturday, 2 May 2015, at 6:37 p.m.
        • OFF TOPIC -- A question of logic
          Mike Clapsadle -- Saturday, 2 May 2015, at 9:04 p.m.
  • OFF TOPIC -- A question of logic
    joe freedman -- Saturday, 2 May 2015, at 4:52 p.m.
    • OFF TOPIC -- A question of logic
      Bob Koca -- Saturday, 2 May 2015, at 4:57 p.m.
      • OFF TOPIC -- A question of logic
        joe freedman -- Saturday, 2 May 2015, at 5:36 p.m.
        • OFF TOPIC -- A question of logic
          Bob Koca -- Saturday, 2 May 2015, at 6:12 p.m.
          • OFF TOPIC -- A question of logic
            joe freedman -- Saturday, 2 May 2015, at 6:21 p.m.
            • OFF TOPIC -- A question of logic
              Bob Koca -- Saturday, 2 May 2015, at 6:44 p.m.
              • OFF TOPIC -- A question of logic
                joe freedman -- Saturday, 2 May 2015, at 6:59 p.m.
                • OFF TOPIC -- A question of logic
                  Bob Koca -- Saturday, 2 May 2015, at 7:17 p.m.
                  • OFF TOPIC -- A question of logic
                    joe freedman -- Saturday, 2 May 2015, at 8:20 p.m.
    • OFF TOPIC -- A question of logic
      Timothy Chow -- Saturday, 2 May 2015, at 6:00 p.m.
      • Coin Flip variation
        Bob Koca -- Saturday, 2 May 2015, at 6:20 p.m.
        • Coin Flip variation
          Timothy Chow -- Saturday, 2 May 2015, at 6:30 p.m.
        • Coin Flip variation
          joe freedman -- Saturday, 2 May 2015, at 7:13 p.m.
          • Coin Flip variation
            Bob Koca -- Saturday, 2 May 2015, at 8:01 p.m.
          • Coin Flip variation
            Art Grater -- Saturday, 2 May 2015, at 8:52 p.m.