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OFF TOPIC -- A question of logic

Posted By: Timothy Chow
Date: Saturday, 2 May 2015, at 6:00 p.m.

In Response To: OFF TOPIC -- A question of logic (joe freedman)

Some of the confusion here is due to semantics. We all have some informal concept of what "accuracy" means, but depending on the precise mathematical definition you choose for that word, you'll get different results.

The definition that is assumed in the problem is that if he is shown a car then he will correctly identify its color 80% of the time. What the puzzle illustrates is that this is not the same as 80% of the time that he mentions a car color, the car will have that color.

One reason for the "standard" definition of accuracy is that it depends only on the observer's powers, and not on the mix of cars in the population.

By the way, there are various ways to quibble with the puzzle. How exactly was the figure of 80% arrived at in practice? Is the observer better at identifying blue cars as blue than at identifying green cars as green? What about red cars? In the context of a puzzle you can assume these things away, but in real life one should be careful about making these assumptions.

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