Effect of Success Probability on Binary Decision Outcomes in Intelligent Systems: A Binomial Distribution Analysis

Abstract

Binary decision-making is central to finance and accounting functions in banks and financial institutions, where outcomes such as approval or rejection are executed under uncertainty. While intelligent systems increasingly provide probability-based recommendations, limited empirical evidence explains how success probabilities translate into actual binary decisions, particularly in developing-economy contexts. This study addresses this gap by examining how success probability influences binary decision outcomes using a binomial distribution framework. A quantitative, explanatory design was employed using data from n = 312 finance and accounting decision-makers in Philippine banks and financial institutions. Logistic regression and binomial modeling were applied to evaluate the relationship between success probability and decision outcomes. Results show that success probability has a significant positive effect on binary decisions (β = 1.872, p < 0.001). Decision consistency increased from 61.3% to 89.6%, while alignment with intelligent system recommendations rose from 58.7% to 92.4% across probability levels. Mediation analysis confirms that decision threshold sensitivity partially explains this relationship (β reduced to 1.204, p < 0.01). The study contributes by empirically demonstrating how binomial probability operates in intelligent–system–assisted financial decision-making, integrating probabilistic modeling with professional judgment. The findings provide practical insights for improving decision-support systems and strengthening governance in financial institutions.