We consider a partial disassembly line balancing problem with hazardous tasks whose successful completions are uncertain. When any hazardous task fails, it causes damages of the tasks on the workstation that it is performed on and all remaining tasks to be performed in the succeeding workstations. We attribute probabilities for the successful completion and failure of the hazardous tasks and aim to maximise the total expected net revenue. We formulate the problem as a two-stage stochastic mixed-integer programme where the assignment of the tasks to the workstations is decided in the first-stage, before the resolution of the uncertainty. We give the formulation for one, two and three hazardous tasks, and then extend to the arbitrary number of hazardous tasks. Our numerical results reveal that proposed stochastic programming models return satisfactory performance and can solve instances with up to 73 tasks very quickly. We observe that the number of tasks, number of hazardous tasks and success probabilities are the most significant parameters that affect the performance. We quantify the value of capturing uncertainty using the expected objective values attained by the solution of the stochastic model and that of the expected value model, and obtain very satisfactory results.