These are the textbooks adopted by my university in the course "probability":
Probability Theory: The Logic of Science by E. T. Jayn
An Introduction to Probability Theory and its Applications, by W. Feller
According to the site of my university, we don´t need any high math background (calculus I, etc).
But i think it may be wrong.
We will study topics like kolmogorov probability, maxwell/poisson distribution and bayes formula.
Thanks for the help.