Here is another textbook which you could try to read: Probability and Statistics by Morris DeGroot and Mark Schervish.
This is from DeGroot’s wikipedia bio:
[DeGroot] wrote six books, edited four volumes and authored over one hundred papers. Most of his research was on the theory of rational decision-making under uncertainty. His Optimal Statistical Decisions, published in 1970, is still recognized as one of the great books in the field. His courses on statistical decision theory taught at Carnegie-Mellon influenced Edward C. Prescott and Robert Lucas, Jr., influential figures in the development of new classical macroeconomics and real business-cycle theory. DeGroot’s undergraduate text, Probability and Statistics, published in 1975, is widely recognized as a classic textbook.https://en.wikipedia.org/wiki/Morris_H._DeGroot
The link above is to a pdf of the 4th ed, published in 2018.
That said, this is a more advanced textbook. Here’s the description from the publisher’s website:
The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data.
Probability & Statistics, Fourth Edition, was written for a one- or two-semester probability and statistics course. This course is offered primarily at four-year institutions and taken mostly by sophomore and junior level students majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.https://www.pearson.com/us/higher-education/program/De-Groot-Probability-and-Statistics-4th-Edition/PGM146802.html
Also note that the link to the pdf above is for a course at Washington University in St Louis titled “Computational Molecular Biology, aka Algorithms for Computational Biology“; you can see from the syllabus that the course starts with a full month of probability. (In fact, you should take a look at the instructor’s “Probability Module Guide“–and the “probability course notes” may be very helpful!)