Evaluating the Strengths and Limitations of Conditional Probability from the Idea of the Three-Door Problem

As one of the most important concepts in probability study, conditional probability plays a key role both in theoretical research and real-world applications. Derived from a famous mathematical problemthe three-door problem (also known as the Monty Hall Problem (MHP)), this paper explores the fundamental idea behind this problem with a consideration of human cognitive bias when they make a choice based on several factors. Additionally, some mathematical proofs will be included with a simulation of the MHP by using some computing skills. Apart from those theoretical concepts, this thesis also includes some evaluations of the strengths and limitations of this mathematical methods (conditionally probability) in real world situations, include medical diagnosis, risk assessment of the supply chain in a country, machine learning concept and lastly decision-making situations under some uncertainty factors which all of them have several dynamic variables that may change randomly all the time (so all the static models cannot handle any of them effectively). Lastly, some future development ideas based on current applications assessments are included in the conclusion part, which provide several criteria that could be further improved to address more complex scenarios and handle human special cognitive bias from their own behavior more properly in the real world in order to increase its overall accuracy.