Drug persistence is a phenomenon by which a small percentage of cancer cells survive the presentation of targeted therapy by transitioning to a quiescent state. Eventually some of these persister cells can transition back to an active growing state and give rise to resistant tumors. Here we introduce a quantitative genetics approach to drug-exposed populations of cancer cells in order to interpret recent experimental data regarding inheritance of persister probability. Our results indicate that alternating periods of drug treatment and drug removal may not be an effective strategy for eliminating persisters.