There has long been debate about whether a first year undergraduate course in discrete mathematics would be better for students than the traditional calculus sequence. The purpose of this question is not to further that debate, but to inquire whether any text has tried to teach calculus by emphasizing probability as a primary motivating example.
It seems that such a text would introduce integrals before derivatives, which I know many authors have tried.
I am asking this question because it seems industry has use for people proficient with probability, and pure mathematics makes great use of these ideas as well (think of probabilistic methods in number theory, for example). It seems that a good course of the above type would be cosmopolitan enough to attract students with tastes in either pure or applied mathematics to major in mathematics.
EDIT: In the absence of a perfect text for this, it may be worth a collaborative effort by mathematicians to write such a text. Is there a way to "crowdsource" writing a text like this as a wiki?