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Parallel machine scheduling is one of the widely studied problems in machine scheduling literature. In this paper, identical parallel machine scheduling problem is considered in the presence of probabilistic processing times and deterministic due dates. In classical scheduling problems, a job is called tardy if it is completed after its due date, otherwise it’s called early. However, in probabilistic concept, a job has a probability of tardiness from 0 to 1. To capture this situation, jobs having probability of tardiness between 0 and 1 are called" risky". If the probability is equal to 0 or 1, job is called early or tardy, respectively. The objective is to minimize the number of risky jobs by keeping the number of tardy jobs minimum. A stochastic non-linear mathematical model is developed. Experimentation is performed with various problem sets jobs. As a result, the proposed model decreased the number of risky jobs and provided a safer schedule than the deterministic model.