Part I. Foundations of Probability: 1. Necessary and sufficient conditions for existence of a unique measure strictly agreeing with a qualititative probability ordering 2. Necessary and sufficient qualitative axioms for conditional probability 3. On using random relations to generate upper and lower probabilities 4. Conditions on upper and lower probabilities to imply probabilities 5. Qualitative axioms for random-variable representation of extensive quantifiers Part II. Causality and Quantum Mechanics: 6. Stochastic incompleteness of quantum mechanics 7. On the determinism of hidden variable theories with strict correlation and conditional statistical independence of observables 8. A new proof of the impossibility of hidden variables using the principles of exchangeability and identity of conditional distribution 9. When are probabilistic explanations possible? 10. Causality and symmetry 11. New Bell-type inequalities for N>4 necessary for existence of a hidden variable 12. Existence of hidden variables having only upper probabilities Part III. Applications in Education: 13. Mastery learning of elementary mathematics: theory and data.