Phenotypic heterogeneity in cancer cells is widely observed and is often linked to drug resistance. In several cases, such heterogeneity in drug sensitivity of tumors is driven by stochastic and reversible acquisition of a drug tolerant phenotype by individual cells even in an isogenic population. Accumulating evidence further suggests that cell-fate transitions such as the epithelial to mesenchymal transition (EMT) are associated with drug resistance. In this study, we analyze stochastic models of phenotypic switching to provide a framework for analyzing cell-fate transitions such as EMT as a source of phenotypic variability in drug sensitivity. Motivated by our cell-culture based experimental observations connecting phenotypic switching in EMT and drug resistance, we analyze a coarse-grained model of phenotypic switching between two states in the presence of cytotoxic stress from chemotherapy. We derive analytical results for time-dependent probability distributions that provide insights into the rates of phenotypic switching and characterize initial phenotypic heterogeneity of cancer cells. The results obtained can also shed light on fundamental questions relating to adaptation and selection scenarios in tumor response to cytotoxic therapy.