Yes, I think you are correct. I would word it this way: Let: {X, 2X} := The amount of $$$ in each envelop A := 1st envelop has $2X B := 2nd envelop has $2X;

Yes, I think you are correct. I would word it this way: Let: {X, 2X} := The amount of $$$ in each envelop A := 1st envelop has $2X B := 2nd envelop has $2X; The flaw in the paradox is to assume that events A and B are independent, when in fact they are mutually exclusive. Now, we can rewrite the whole "(0.5 A) + (0.5 A'/2) /= 5/4 A" nonsense as: P(A|B)2X + P(B|A)X = 02X + 0X = 0 Which is zero because it only covers half of the probabilities space, the other half is where all the density of the probability function lies. P(A|B')2X + P(B|A')X = 0.52X + 0.5X = 3X/2; which is what we would expect by intuition, halfway between the 2 prizes.