There is no probability - you can't apply probability theory at all since it's easy to make "Dutch Book" against any numerical answer (this can be accomplished

There is no probability - you can't apply probability theory at all since it's easy to make "Dutch Book" against any numerical answer (this can be accomplished by selecting the initial pool of 1000 as you please.) All this hinges on: "All they know is that 900 people said it was blue, and 100 did not." Meaning, those who are being asked for a probability don't know who selected those people or how. This crops up with many false descriptions of the "Monty Hall Paradox" as well. Some descriptions also allow Dutch Book defeats, so probability can't be applied to the problem as it is (falsely) described. The principle here is that you can't and shouldn't apply probability to questions about a deck of cards, if someone else can select which cards are in the deck, including 52 copies of the same card, either before or after your guess or bet. They'll take your money. When Anderson et al changed the meaning, mid-game, of "Triple A rating" for subprime bonds, etc, before 2008 they pulled exactly this sort of trick; thus fooling those who thought they could apply calculations of probability to a situation where probability didn't apply; since the only thing that mattered was some executive's guess about how likely it was that he would end up in jail for rigging the system. (Not at all likely, we know now!) When I was young there were a lot of "nine out of ten doctors recommend our cigarettes" ads also based on the same trick, and it must have worked on a lot of people, 'cause it was very common. As with the common misdescriptions of the Monty Hall Problem, it's possible the writer meant to describe a quite different problem, but as the problem is described here no probability can be inferred.