a lot of the comments here are critical of the way these scenarios are presented, but I don’t believe there is in fact any deep issue.
the fact of the matter remains, if you are in a situation where you have two things which you do not yet have the information to differentiate, and you know they have a state in some binary property, and that this state for one is independent of the other. Then, if you learn, by any means, that one of these objects has a specific state (call it A) with regard to the binary property, your probability needs to adjust to p(both are in state A|one is in state A) = 1⁄3 and p(only on object is in state A|one is in state A) = 2⁄3.
johnclark just used a classic example to demonstrate the importance of how interchangeability has a large and unintuitive effect on probability.
It is my contention that the sentiment this scenario is unintuitive because of the way johnclark is incorrect. I have seen this question posed in other ways to classes of smart college students studying probability and most of them getting it wrong. External knowledge of the way people tend to provide information isn’t really a relevant factor here.
This article is well written and important, and by no means deserves the very low karma score it has received (-6 as of this writing, −7 before my vote)
a lot of the comments here are critical of the way these scenarios are presented, but I don’t believe there is in fact any deep issue. the fact of the matter remains, if you are in a situation where you have two things which you do not yet have the information to differentiate, and you know they have a state in some binary property, and that this state for one is independent of the other. Then, if you learn, by any means, that one of these objects has a specific state (call it A) with regard to the binary property, your probability needs to adjust to p(both are in state A|one is in state A) = 1⁄3 and p(only on object is in state A|one is in state A) = 2⁄3. johnclark just used a classic example to demonstrate the importance of how interchangeability has a large and unintuitive effect on probability. It is my contention that the sentiment this scenario is unintuitive because of the way johnclark is incorrect. I have seen this question posed in other ways to classes of smart college students studying probability and most of them getting it wrong. External knowledge of the way people tend to provide information isn’t really a relevant factor here. This article is well written and important, and by no means deserves the very low karma score it has received (-6 as of this writing, −7 before my vote)