2-12 is contained in 1-12.
The fact that 1 occurs with probability 0 is an example of the point I was making (how you make your random choice affects the probabilities).
So why doesn't it choose between rolling -infinity to +infinity with all numbers other than the natural numbers including and between 2-12 having a probability of 0? I don't think you can say that one exists in the set with a probability of 0, for it to exist it then has a probability. Its defined by the number of occurrences of the element divided by the total number of elements in the set. The probability of a 2 is 1/36 because the outcome of 2 only occurs once out of the 36 possible outcomes while 7 occurs six times out of 36 so its probability is 1/6. 1 however, doesn't exist within the set of outcomes and so its not that it has a probability of 0 its probability is null/undefined. If you asked the set whats the probability of 2 it would say "1/36". If you asked it whats the probability of 1 it wouldn't say "0/36", it would say "what the **** is a 1?"
Now I could be wrong on this because the probability and statistics class I took was 3 years ago, but I remember thinking that nothing can ever be 0. For something to be 0 it must exist but not exist, so its either asymptotically 0 or is null/undefined. To say a probability is 0 then you have either calculated the probability wrong or you are not handling the set you think you are and are not thinking within the scope of the set you believe to be talking about. Its like applying the think therefore I am mentality to the set. If the set can suggest 1 is a probability of 0 then it has created a paradox, because now that the 1 exists within the scope of the set it can no longer be 0. It thought of a 1 so there now is a 1, its probability may be so incredibly low it approaches 0 but it can't be a 0. Unfortunately, given the conditions and using the defined addition operation, it is impossible for 1 to exist in the outcome set so it is impossible to consider its probability when discussing the outcomes from the view of the set itself.
You can't make something out of nothing, 1s will never appear randomly out of nowhere in a set that doesn't have them, therefore the universe is deterministic.