The phenomenal growth in the use of internet-based technologies has resulted in complexities in cyber security subjecting organizations to cyber-attacks. This research is purposed to develop a cyber-security system that uses the Bayesian Network structure and Machine Learning. The research determined the cyber-security framework appropriate for a developing nation; evaluated network detection and prevention systems that use Artificial Intelligence paradigms such as finite automata, neural networks, genetic algorithms, fuzzy logic, support vector machines, or diverse data-mining-based approaches; analyzed Bayesian Networks that can be represented as graphical models and are directional to represent cause-effect relationships; and developed a Bayesian Network model that can handle complexity in cybersecurity. The Pragmatism paradigm used in this research, as a philosophy is intricately related to the mixed-method approach, which is largely quantitative with the research design being a survey and an experiment, but supported by qualitative approaches where Focus Group discussions were held. The Artificial Intelligence paradigms evaluated include machine learning methods, autonomous robotic vehicles, artificial neural networks, and fuzzy logic. Alternative improved solutions discussed include the use of machine learning algorithms specifically Artificial Neural Networks (ANN), Decision Tree C4.5, Random Forests, and Support Vector Machines (SVM).