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Normally, when the concentration of the products isn't given for equilibrium problems and only reactants are presented initially, it is assumed products have very low concentrations that would make solving the problems to be more complex. Essentially, to make calculations easier and less complicated, we assume that the concentrations are so low, that they can be estimated to be 0.
We also have no reason to believe there is already product at the start unless it is explicitly stated. If these were actual reactions we were doing in a lab, we could probably measure the initial conditions, but since it's a hypothetical problem, I don't think we can actually determine the initial conditions unless more information is given, so we have to assume for convenience.
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