HARNESSING PROBABILITY THEORY TO IMPROVE AUDIT SAMPLING STRATEGIES AND OPTIMIZE RESOURCE ALLOCATION

This study explores the application of probability theory in audit sampling strategies to optimize resource allocation and enhance financial irregularity detection. The research employs a mixed-methods approach, integrating quantitative statistical analysis with qualitative insights from audit professionals. Empirical data from 2020 to 2024 reveal that probability-based sampling methods reduced audit costs by an average of $20,000 annually while improving detection rates by 12% compared to traditional sampling techniques. Regression analysis indicates a strong negative correlation (R² = 0.87) between sample size reductions and cost savings, confirming the efficiency of probability-driven approaches. Additionally, a t-test (p = 0.03) highlights a significant reduction in audit duration, decreasing completion times by an average of 5 days. The overall Pearson correlation coefficient (0.91) underscores the strong alignment between probability driven audit sampling and enhanced audit efficiency. The study concludes that integrating probability based models into auditing frameworks significantly optimizes resource utilization and strengthens financial oversight. It recommends increased auditor training, adoption of AI-powered audit tools, and regulatory collaboration to facilitate the widespread implementation of probability-based sampling in modern auditing.