Even this isn't 100% accurate since, as pointingdogs stated, this isn't a random drawing and the winners are removed from the draw along with all of their chances. So your actual odds are going to be slightly better than the calculation above, but since we have no way of knowing who is going to be drawn in the actual drawing, much less the bonus points that the lucky winners hold, the calculation above will get you a respectable number.
Does that help? You probably now want to bang your head against the wall....
Everything he did looks good. In the past I set up a somewhat basic simulation and set it to run 100 thousand times (Turns out you can get reasonably close by running it far less than that too.). That saved me difficult math at the cost of tying up my background computer processes for a while.