Reddit mentions of Introduction to Probability (Chapman & Hall/CRC Texts in Statistical Science)

Sure! I have a lot of resources on this subject. Before I recommend it, let me very quickly explain why it is useful.

Bayes Rule basically means creating a new hypothesis or belief based on a novel event using prior hypothesis/data. So I am sure you can already see how useful it would be in medicine to think about. The Rule(or technically theorem) is in fact an entire field of statisitcs and basically is one of the core parts of probability theory.

Bayes Rule explains why you shouldn't trust sensitivity and specificity as much as you think. It would take too long to explain here but if you look up Bayes' Theorem on wikipedia one of the first examples is about how despite a drug having 99% sensitivity and specificity, even if a user tests positive for a drug, they are in fact more likely to not be taking the drug at all.

Ok, now book recommendations:

Basic: https://www.amazon.com/Bayes-Theorem-Examples-Introduction-Beginners-ebook/dp/B01LZ1T9IX/ref=sr_1_2?ie=UTF8&qid=1510402907&sr=8-2&keywords=bayesian+statistics

https://www.amazon.com/Bayes-Rule-Tutorial-Introduction-Bayesian/dp/0956372848/ref=sr_1_6?ie=UTF8&qid=1510402907&sr=8-6&keywords=bayesian+statistics

Intermediate/Advanced: Only read if you know calculus and linear algebra, otherwise not worth it. That said, these books are extremely good and are a thorough intro compared to the first ones.

https://www.amazon.com/Bayesian-Analysis-Chapman-Statistical-Science/dp/1439840954/ref=sr_1_1?ie=UTF8&qid=1510402907&sr=8-1&keywords=bayesian+statistics

https://www.amazon.com/Introduction-Probability-Chapman-Statistical-Science/dp/1466575573/ref=sr_1_12?s=books&ie=UTF8&qid=1510403749&sr=1-12&keywords=probability

I'm going to guess this one based on high reviews and a description that mentions R.

I’d recommend Blitzstein’s Into to Probability book- it’s the book used for Harvard’s Stat110 which has free lectures online as well.

https://www.amazon.com/Introduction-Probability-Chapman-Statistical-Science/dp/1466575573

I have very few universal recommendations. Think the only one that actually comes to mind is "Introduction to Probability" by Blitzstein and Hwang. It is probably the best book on probability that I've found for a broad audience. It also has a corresponding video lecture series.

If you want any more, please answer this:

• What is your interest?
  
• What is your background?
  
• What do you want to learn to do?
  
  Maybe I can see what I have laying around that meets your criteria.
  

The Nature of Computation

(I don't care for people who say this is computer science, not real math. It's math. And it's the greatest textbook ever written at that.)

Concrete Mathematics

Understanding Analysis

An Introduction to Statistical Learning

Numerical Linear Algebra

Introduction to Probability

I really loved Harvard Stat 110 (both the book and the videos for the lectures)

Blitzstein and one of his students published a probability textbook

At least re: random variables, events, PDF, and CDF, I like the diagrams from Prof. Joe Blitzstein's textbook:

http://i.imgur.com/aBkgHGC.jpg

I found Prof. Joseph Blitzstein's course, at Harvard, on statistics engaging. First I watched his lectures and worked through the problem sets. This was extemely rewarding, so I went on to work through his book on probability. According to me, what separates him from other Profs is that he takes a lot of effort to build intuition about statistical concepts.
Stat110 is the course website. You can find his book here.