No. That you are in a cubicle is a given fact, so the probability that you find yourself in a cubicle is unconditionally 1.
But it's not 1 that you would be in a cubicle at all. The paradox disappears if the problem was formulated like this: "God shuffles DNA and there is 0.0000000000001 chances tha it shuffles up you and he does that for every cuebicle". Or: "God create you first, then flips a coin and put you at random in one of the created cubicles".
Formulation of the problem should mention which one is it. If it doesn't we are back to guessing what God does (similarly to 2 envelope problem which comes down to guessing what the sponsor's preferences for amounts are). As there are infinitely many ways God could decide to create humans in cubicles you can't answer that without giving some guess (priori) for probability distribution over those choices.
The way the problem is presented, it is a given that you're in a cubicle. If you wanted to be more explicit about it, you could say that God, before creating humanity, flipped a coin, and then created either 10 or 100 humans and placed them into cubicles. You wake up and have to estimate the probability of that coin flip.
So the doomsday argument is actually correct. :-) But it's really nothing more than the (IMO vacuous) observation that (say) half of the people who ever live will have a birth order number greater than the median, and so the odds are 50-50 that fewer people will be born after you than before you. More generally, the odds that N times as many people will be born after you as before you is equal to 1/2N.
>You find yourself in one of the cubicles and are asked to guess whether there are ten or one hundred people? Since the number was determined by the flip of a fair coin, and since you haven’t seen how the coin fell and you don’t have any other relevant information, it seems you should believe with 50% probability that it fell heads (and thus that there are a hundred people).
The conclusion in the last sentence is incorrect is an incredibly subtle way. Since 10 times more people are in cubicles in the heads case, the probability that you find yourself in a cubicle at all is ten times higher in that case, which affects your prior. By Bayes' theorem:
P(HEADS| WAKE UP) = (P(WAKE UP|HEADS) * P(HEADS)) / ( P(WAKE UP |HEADS) * P(HEADS) + P(WAKE UP|TAILS) * P(TAILS) )
= (10 * P(WAKE UP|TAILS) * P(HEADS)) / ( 10 * P(WAKE UP|TAILS)* P(HEADS) + P(WAKE UP|TAILS) * P(TAILS) )
= 10 / (10 + 1)
= 10 / 11, or about 91% chance of heads given that you find yourself in a cubicle.