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Interesting you throw that accusation given that you do exactly the same thing when analyzing the EPR experiment. Note: this example was designed to reveal precisely this kind of misunderstanding. Now it is you making the argument which you have repeatedly rejected without understanding. I'm happy you are getting the point, which you have repeatedly refused to understand when I made it. Now you are forced to make the argument yourself when faced with an obviously local and realistic example which violates the inequalities.Yes. In your 'proof' the inequality applies to averages from the same series of [itex]\{a_i,b_i,c_i\}[/itex], where the average is defined as arithmetic mean of all elements in the series, even though you did not explicitly state it. It does not allow you to pick different subsets to calculate <ab>, <ac>, and <bc>. But of course, since you did not articulate your proof, you have missed this. If, instead of handwaving, you actually try to write out the steps, this is as far as you can get.

Really DK? I thought you knew better than to make such a ridiculous claim:Bell's inequality, on the other hand, applies to expectation values. It is a high time you learn the difference between the two.

Now even a cave man can understand that <ab> is the expectation value of paired product of outcomes a*b for a pair of dice thrown a very large number of times, just like in the OP example.Wikipedia said:Theexpected valuemay be intuitively understood by the law of large numbers: the expected value, when it exists, is almost surelythe limit of the sample mean as sample size grows to infinity. More informally, it can be interpreted as thelong-run average of the results of many independent repetitions of an experiment(e.g. a dice roll).

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In quantum mechanics, theexpectation valueis thepredicted mean value of the result(measurement) of an experiment.

*You*need to learn about expectation values, einstein. I did not hear you complaining that Aspect, or Weihs, etc calculated averages from their experiments not expectation values. Such a suggestion will be laughed at, or rather cried at.