logic: proof problem

Seems fallacious via over simplification to me. seems like the math would need to account for the random things that will happen. but i guess the argument itself doesnt matter, just the abstract math being applied to the objective world. Somehow this can be seen as useful even without the infinite variables accounted for?

I wrote a long answer but my computer crashed and I cannot be bothered to write it again. I did a check of the argument using truth tables, and it is valid (if I did the table correctly).

http://img209.imageshack.us/img209/1659/truthtableproof.jpg