Do you think that since the witness's correct rate is 80%, the color of the taxi is 80% likely to be blue? So the color of the taxi is blue.
If you think so, then you have made the mistake mentioned by the author Daniel Kahneman in his book Thoughts, Fast and Slow, and neglected the fallacy of the benchmark ratio, that is, the basic proportion of "blue-green" cars in this city has not been taken into account.
When it comes to the fallacy of basal rate, we'd better start with the famous Bayes theorem in probability theory. Thomas Bayes (070 1-176 1), a British statistician, used to be a priest. This Bayesian theorem was not created by him before his death. Although Bayesian theorem is the product of18th century, it has been used for 200 years, and I don't want to meet the challenge in 1970s. This challenge comes from the "basic probability fallacy" put forward by Daniel Kahneman and amos tversky. Daniel Kahneman cited the example of taxi in his thought, which inspired people to think about the reasons why people are not sensitive to the basic ratio and affect their "decision-making".
Let me ask you again, do you think more people buy mineral water or Chanel perfume?
God, isn't the crowd and demand rate obvious? This is not a problem at all, but people often evaluate probability through representativeness. For example, if A can highly represent B, people will think that A's high probability originates from B, but if A and B are not similar, people will think that A originates from B's probability base.
Kahneman put forward a hypothesis that if people evaluate probability through representativeness, then the basic ratio will often be ignored.
Going back to the color of the car that just happened, what the witness said is very doubtful. Not 80% of the time is blue, but 4 1% of the time is blue. The probability that the car will be green at the same time is 59%. Therefore, the vehicle color of the accident that day is likely to be green. After all, the basic ratio is 59%.
How to calculate the above data by Bayesian theorem is a bit too complicated. It is difficult for me to discuss in depth and explain systematically and clearly those who have poor math scores here. Interested friends can have a search online.