So yesterday I saw this video with the monty hall problem, where you have 2 goats and a car each behind a door, each door having 1/3 chance of having the car, we choose door A to win the car, door B with the goat is revealed, so now doors A and C dont have 1/2 chance of having the car as intuition would say, but 1/3 for door A and 2/3 for door C . So I started thinking if there is some equivalent quantum experiment of the monty hall problem. And apparently there is: http://arxiv.org/pdf/quant-ph/0202120v1.pdf and http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652006000300003 I havent tried to understand the first paper, but the second one says "Starting from the an initial "equiprobable" state (with the natural choice M1,2 = for the measurement operators) leads to identical conclusions, concerning the MHP puzzle, as in the classical probabilistic reasoning. It is remarkable that the argument leading to these conclusions seems to be more straightforward in the quantum than in the classical setting. It is perhaps not too farfetched to assert that the correct answer to the MHP puzzle is "embodied" in the very formalism of quantum mechanic's measurement theory. " But wouldnt that mean that in the quantum world just like in the classical world, probabilities are just a mathematical tool that only affects our state of knowledge and have no bearing on what is actually going on ?