It would greatly depend on whatever means had caused said zombie apocalypse..

That , and more importantly HOW it is spread.... and the contagion of it.
If even coming in contact with body fluids of the "infected" would get you dead..

If the above was KNOWN , then it would be much much easier to survive .

If it is unknown or highly contagious, then I'd say one's chances of survivability are slim to none ..