The authors discuss how the description of a two-particle spin-1/2 system prepared in a singlet state, a product state of definite total spin-projection and a specified mixture relates to the EPR conceptions of reality, locality and completeness and to Jarrets interpretations and representations of these concepts by probability statements. The importance of the state-preparation procedures and their relevance in this context is emphasized. The position of Bell`s inequalities is also discussed. It is concluded that the inequalities have a limited power in deciding whether or not a system requires a quantal description, and that making a priori claims on reality and completeness is a too narrow scheme to describe quantal phenomena. 21 refs., 4 figs.