Possible typo:

A theory about the laws of physics governing the motion of planets, devised by Sir Isaac Newton, or a theory simply stating that the Flying Spaghetti Monster pushes the planets forward>s< with His Noodly Appendage.

In the spirit of aiming low, I don't think you aimed nearly low enough. If I hadn't already read a small amount from the sequences I wouldn't have been able to pick up too much from this article. This reads as a great summary; I am not convinced it is a good explanation.

The rest of this comment is me saying the above in more detail. Do note that this is my perspective. Even a newb such as myself has been tainted with enough keywords to being inferring details that are not explicitly mentioned. This critique is massively excessive compared to the quality of the work. This means that you did a good job but I went all pesky-picky on you anyway.

You've probably seen the word 'Bayesian' used a lot on this site, but may be a bit uncertain of what exactly we mean by that. You may have read the intuitive explanation, but that only seems to explain a certain math formula.

I don't know which is a more successful way to talk to people: Using "you" or not using "you." Rephrasing those two sentences without the word, "You:"

The word "Bayesian" is used a lot on this site but it is a difficult concept to fully grasp. There is an intuitive explanation, but it focuses on the math behind the concept.

And so on. What I like about your opening:

• Links to previous descriptions
• Lets the reader know that the Bayesian concept is deeper than math. Math is at the core but for people who are scared of Math another way to think about the subject is possible.
• Notes that the concept is difficult to understand because it is difficult to understand, not because the reader is an idiot

Things I don't like:

• As much as I like the intuitive explanation, starting with Math is bad for people scared of math. Even bringing it up can shut them into a, "Oh no, I won't be able to understand this," mode. I don't know if there is a better way to say what needs to be said, however.
• "You," in this case, is a little patronizing. Not a big deal; just a minor point.
• Too defensive. The first couple paragraphs are trying to convince the LessWrong crowd that this explanation is needed. That is good, but the final edit should probably leave it out. The intended audience is much, much lower than that.
• There is no mention of the Simple Truth or an equivalent starting ground. This may not be needed, but it sure helped me get into the right mindset when starting the sequences.

We'll start with a brief example, illustrating Bayes' theorem. Suppose you are a doctor, and a patient comes to you, complaining about a headache. Further suppose that there are two reasons for why people get headaches: they might have a brain tumor, or they might have a cold. A brain tumor always causes a headache, but exceedingly few people have a brain tumor. In contrast, a headache is rarely a symptom for cold, but most people manage to catch a cold every single year. Given no other information, do you think it more likely that the headache is caused by a tumor, or by a cold?

I would drop the term "Bayes' theorem" here. "We'll" is another example of, "You." This paragraph could be touched up a bit but I feel this is more me noticing that my writing style is different from yours.

I am not sold on this being a good first example. I like that it is something that most people will identify with, but the edge cases here are nuts:

• There are more than two reasons for headaches
• Do brain tumors always cause a headache?
• I don't normally get headaches from colds and don't normally associate headaches with colds. When pondering why I have a headache, "colds" is pretty far down the list.
• More than "exceedingly few" have brain tumors. A heck of a lot more people have colds but "exceedingly few" doesn't immediately translate into "more people have colds."
• Is the type of headache from a brain tumor the same type of headache from a common cold? This doesn't matter to you, since you don't actually care about the details of the headache, but a reader may very well offer this suggestion as a solution to figuring out if the headache is from a brain tumor or a cold. People like to stick unnecessary details into examples because that is how they solve real-world examples. At this point in the article, they don't care about the example. They are imagining someone with a cold.

Given the chance, I would reword the paragraph as such:

A simple example can be found when someone asks a doctor why they have a headache. The doctor knows that a typical cold will only sometimes cause headaches. The doctor also knows that a brain tumor will almost always causes headaches. If the doctor compared these two causes and decided that it is more likely a brain tumor is at fault, then something went wrong. If you walked into a doctor's office complaining of a headache and were immediately diagnosed with a brain tumor, you would probably be a little suspicious. Bayes' theorem helps us explain what, exactly, went wrong and how to fix it. It uses math to do it, but the basic concept is easy to understand.

Do you want more of this? If not, I can stop now. If so, I can continue later. If you'd like something similar but much shorter and concise, I can do that too.