I recently came across 3blue1brown's YouTube short on Laplace's Rule of Succession, as well as his two videos on the probability of probabilities. In these videos, he uses the example of Amazon reviews to explain how Laplace's Rule of Succession can provide a better estimate of the likelihood of having a positive experience with a specific seller. The rule suggests adding one positive and one negative review to the available data and then calculating the overall rating.
I'm interested to know whether Laplace's Rule of Succession can also be applied to evaluate a student's performance in solving problem sets. Specifically, I'm curious if adding one positive and one negative data point to the existing sample could provide insights into their effective performance. Currently, I am preparing for a board examination similar to the PE Engineering Exam, and I believe tracking my performance using this rule might be helpful.
I'm wondering if the underlying assumption of Laplace's Rule of Succession, which assumes a constant true probability for an event (such as an Amazon seller's rating), still holds true when analyzing a student's historical performance data in solving problem sets (e.g., 21/25, 43/50, 72/75, etc.). While the true probability of a student's performance may change over time as they improve their understanding of a subject, the original assumption remains valid for a specific point in time. I believe this motivation could also apply to general student grades, and I would like to learn more about it.