Applied Mathematics the foundational discipline that guides everyone to ensure the findings are indeed backed by reality. As scientists we're primarily interested in probability interpretations.
Probability has a few approaches that have been taken over time. The subjective approach is where humans intuition is met and where you typically enter a problem. We need to move to more data driven methodologies which started with Classical, then Frequentist and Propensity blend into the mix ref
Subjective 
Classical 
Frequentist 
Propensity 

Main hypothesis 
Degree of belief 
Principle of indifference 
Frequency of occurrence 
Degree of causal connection 
Conceptual basis 
Knowledge and intuition 
Hypothetical symmetry 
Past data and reference class 
Present state of system 
Conceptual approach 
Subjective 
Conjectural 
Empirical 
Metaphysical 
Single case possible 
Yes 
Yes 
No 
Yes 
Precise 
No 
Yes 
No 
Yes 
Problems 
Reference class problem 
Ambiguity in principle of indifference 
Circular definition 
Disputed concept 
Subjective Intuition is based on personal opinions, interpretations, points of view, emotions and judgment. It is often the genesis for human innovations and a healthy component of human logic that can form hypothesis’s that can be proven by more mature mathematical approaches. Note: considered illsuited for scenarios like news reporting or decision making in business or politics.
Classical Probability was developed from studies of chance. It states that probability is shared equally between all the possible outcomes, provided these outcomes can be deemed equally likely.^{[1]}
Frequency probability of an event to occur in future is related to frequency of occurrence in past if repeating a process a large number of times under similar conditions.
 Classical probability would say there's a 50:50 chance on every coin flip regardless of history
 Frequency probability would take into account the historical trends to predict the future
Predictive modeling is an area of study to help humans leverage advanced mathematical approaches to find patterns in the historical data upon which future predictions can occur.