The "Intuitive Explanation" is very interesting, but not always the easiest to grasp. The most important thing to understand the Sequences is the beginning, understanding how to compute (even if you do it manually, by "counting" women of each possible cases) the chance of having cancer knowing you have a positive mammography.
For the rest, I would advise you to start reading the Sequences, and stopping when you find something that you don't understand, and then trying to learn that part of maths. You're free to ask for pointers or hints when you find such a "blocker".
What you'll need is base of probability theory, a tiny bit of vector algebra (or anything that can help you grasp the concept of n-dimensional space, with a huge n) for the quantum mechanics sequence, and the understanding of what a "function" is in maths. The rest should go easily.