Resource allocation is a typical topic within operational research and the theory of algorithms. Generally, the objectives of resource allocation involve optimizing time or resource effectiveness for a task, or maximizing the likelihood of successful task completion. There are various approaches to solving these problems. This study addresses the problem of allocating a given amount of resources among multiple working units operating in parallel. As a measure of effective problem-solving, we approach resource allocation in a more stochastic manner, using the probability of at least one of the parallel working units completing the task. For this purpose, we propose a versatile parametric version of the probability that a given working unit fails to complete the task. Inspired by real-world practices, we observe that the probability of an individual working unit failing to complete the task typically decreases as the allocated resources increase. On one hand, allocating the maximum possible resources to a single working unit minimizes the probability the unit fails the task finishing. On the other hand, employing multiple units in parallel increases the overall likelihood of task completion, despite each unit receiving only a portion of the total resources. In this paper, we (i) determine the optimal number of working units to maximize the probability of at least one completing the task, and (ii) explore optimal strategies for dividing the given amount of resources among them. Finally, we discuss potential applications of our approach across various fields related to resource allocation and optimization.