It is well known that ideal projective measurements are paradigmatic non-deterministic and irreversible processes in Quantum Mechanics. Nevertheless it is also known that the associated probabilities satisfy a time-symmetry property: the conditional probabilities for prediction and retrodiction take the same form. I shall argue that this feature of Quantum Mechanics may be used to discuss it in a more natural way and to present it as a less mysterious theory than is usually done. This will be shown for the Algebraic Formulation and the Quantum Logic Formulation. If time permits, I shall ask some naïve questions about the Quantum Information Formulations and Quantum Gravity.