Math error in Brian Greene book?

Factual Questions
21

doors are labeled 1,2,3
We have 3^2 combinations namely
(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)

If the boxes were pre-programmed and say the program is (blue, red , blue ) for doors (1,2,3)
then we have :
(blue,blue),(blue,red),(blue,blue),(red,blue),(red,red),(red,blue),(blue,blue),(blue,red),(blue,blue) 6/9=2/3
If the program were (Red,red blue) the ratio is unchanged , but the colour combinations will be different

But if they are not programmed , combinations (1,1),(2,2),(3,3) give the same colour but they would have no idea about; would have happened had they opened different doors , say the combination 1,2 which gives (blue,blue) in the first program , but the same combination give (blue red ) in the second program .

That implies the two(or more ) programs superimposed in these non-symmetric combinations. The the probability for Same colour, in those combinations, cancel the probability for different colours , leaving us with 3/9=1/3 certainity about colour similarity namely in combinations that involved opening the same door . Which means that the probability of combination (1,2),(1,3),(2,1),(2,3),(3,1),(3,2) is undecided 50/50 %
So we have 2 different doors A,B , and two colours Red and blue , 2^2=4
Red Red
Blue blue
Red blue
Blue Red X 6 combinations = 24

the 6 combinations expand into 24 colour combinations . 12 combinations show the same colour , and 12 show different colours , and they cancel to Zero leaving us with 1/3 certainity about colour similarity + 0.5 probabillity for colour similarity

It’s probable that the experiment would yield each of the 6 combinations in one colour red/blue for 6 boxes. But as the number of trials increase , opposite probabilities cancel , and limit to zero .

22

I’m too lazy to do it again, but the first time I read Greene’s book I was convinced. This isn’t so much about Aspect’s experiment as about Bell’s theorem which I also reasoned out once upon a time.

If you want a real howler in a book by a well-known physicist read about “Newton’s error” in an appendix to Alan Guth’s book on inflation theory. Newton was absolutely right and Guth absolutely wrong. You cannot generalize from finite spaces, no matter how large, to an infinite space.