Screen reader help for "the region {(x, y)|x + y ≤ 1}" (Series of screen reader related questions on basic symbology)
"the probability that x, y are in A where A is the region {(x, y)|x + y ≤ 1}."
How should I write this out the bolded section to that a screen reader will read it correctly?

As I understand it, if you're concerned about screen readers for math, you shouldn't be using {(x, y)|x + y ≤ 1} with some sort of accompanying text that 'explains' your notation in some special way for non-sighted readers (as one might for .jpg images relevant to your mathematical content). 
You should use either raw MathML directly in your markup; or else use a plug-in like MathJax and let it render the MathML from the LaTex for $\{(x, y) \mid x + y \leq 1\}$ (which uninterpreted would be '\{(x, y) \mid x + y \leq 1\}'. Then most screen readers will be able to communicate this to your end user in a consistent way.
Note that it might still be useful (depending on context) to also include the sort of verbal explanations such as those suggested by other Answerers; to the extent that it might be helpful to all your readers.
I think it's easy as a sighted reader to think that:
$$\sum_{x=0}^{k}\frac{n-k \choose k}{k+1}$$
is somehow inherently a 'visual' statement; but screen readers can handle this if it's in the proper format. Here, the LaTex is '\sum_{x=0}^{k}\frac{n-k \choose k}{k+1}' and with a bit of practice, it's just as easy (or hard!) to understand for a non-sighted mathematician as a sighted mathematician.
And I guess that's the bottom line to me - if you think there's something more to say (in a mathematical sense) than is expressed by $\{(x,y) \mid x+y \leq 1 \}$, then there's no particular reason to think that a sighted mathematician will understand your intent more or less than a non-sighted one would; as long as you use a reasonable syntax.
