I have to teach a Calculus class (details on the syllabus below) and I want to add some applications to other sciences. But I would like to avoid the classical physics examples, because the physics teacher will be way better than I am to explain beautiful physics. So I decided to try to teach some probabilities (with maybe some statistics) to my students to keep them motivated.
For example, the computation of the mean of a geometric distribution involves the computation of a series.
Unfortunately, the only references I know for probabilities use Lebesgue integrals. Do you have any recommandations for a probability book which would use only Calculus materials (beside the usual combinatorics materials) and no deep analysis tools? Basically, something for University 1st or 2nd year or engineer major?
Syllabus: what my students know or will learn during this course (roughly Chapter 1 to 11 of Stewart's Calucus): continuity, derivatives and integrals; applications of integrals (volume, arclength,...); basics on parametric curves and polar curves; methods 1st and 2nd order differential equations; series and power series.
PS: books would preferably be in English but Spanish or French is also acceptable.