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Every scientific idea—whether in medicine, architecture, engineering, chemistry, or any other field—when implemented, is prone to small errors and uncertainties. Mathematics, through the lens of probability theory and statistical inference, aids in precisely managing and thereby mitigating these uncertainties. It must always be considered that in all practical scenarios, "the outcomes also depend on many other external factors to the theory," be they initial and environmental conditions, experimental errors, or others.

The uncertainties surrounding these factors render the theory-observation relationship probabilistic. In medical practice, two types of uncertainty predominantly impact diagnoses: subjective uncertainty and causality. Therefore, in this context, it becomes crucial to differentiate between these two uncertainties and to demonstrate that the concept of probability assumes different meanings in these contexts. We will endeavor to elucidate these concepts by connecting each critical step to the clinical approach that has been documented in previous chapters, particularly focusing on the dental and neurological domains in vying for diagnostic supremacy for our dear Mary Poppins.