Platinum drugs and PARP inhibitors (PARPis) are considered to be effective to BRCA-associated cancers, in which DNA repair is impaired. These agents cause stalled and collapsed replication forks, and create double strand breaks efficiently in the absence of repair mechanisms, resulting in arresting cell cycles and inducing cell deaths. However, recent studies have shown that the chemotherapy failed due to the emergence of drug resistance. In this study, we develop a stochastic model of the BRCA-associated cancer progression, in which there are four cancer populations with: (i) functional BRCA, (ii) dysfunctional BRCA, (iii) functional BRCA and a growth advantage, and (iv) dysfunctional BRCA and a growth advantage. The four populations increase in number from one cancer cell with normal repair function until the total number reaches a detection size. We derive formulas for the probability and the expected number of each population at the time of detection. Furthermore, we extend the model to consider the tumor dynamics under treatment. Results from the model are validated with good agreements with the clinical and experimental evidence in BRCA-associated cancers. Based upon the model, we investigate the condition in which the emergence of drug resistance under treatment is originated from either pre-existing intrinsic drug resistant population or de novo population by secondary mutations, and identify the condition of effective treatment by platinum drugs and PARPis. Our results imply that different types of cancers have a preferential way of acquiring resistance to platinum drugs and PARPis according to the growth and mutational characteristics.