I am sorry, but this is completely wrong and the following calculation is flawed. It is as if you had a water well containing 100 liters of water and thought you could get it completely dry by pulling out 10 buckets of 10 liters from it. In the same way as water continues to flow into the well the faster the more water you pull out (with the gradient of levels between the well and the phreatic water), also CO2 from the body flows into the lungs the more the deeper you breathe. The alveolar partial pressure of CO2 does not change a lot, and is almost pretty constant. You can lower it with serious hyperventilation, when you manage to lower the stock of CO2 in entire body, but normally you rather want to avoid it.
The gas, both O2 and CO2 moves in the lungs thanks to diffusion (with the difference of partial pressures in individual parts), not really with ventilation. Hence, the depth of the breathing plays much smaller role than it looks like. Breathing normally will result in PAO2 (Partial Alveolar pressure) of some 100 mmHg (around 13%), while with extreme hyperventilation you may manage blowing off around 4% of the alveolar CO2 (being still continuously repleted from the body). At moderate hyperventilation, or few purges, the difference in alveolar percentage will be even lower, while the lowering of CO2 in body may be still important.
Now, there are other effects of the purges and hyperventilation, that may (under certain conditions and to some extent) increase the stock of oxygen in your venous blood, but there are also negative effects of the low CO2 - hence when you decide for hyperventilation (and purges are nothing else than that), a very careful balance is needed. This was discussed in depth in other threads about hyperventilation, so I won't repeat it here again.