On practical problems with the explanation of the difference between possibility and probability

In his famous paper "Fuzzy Sets as a Basis for a Theory of Possibility" (Zadeh, 1978) Professor Lofti Zadeh intro- duced the notion of possibility distributionX and the concept of possibility measure. He defined in the paper the possibility distrib- ution function to be numerically equal to the membership function (�X = µF ). In this paper Professor Zadeh draws the special atten- tion of the reader to the fact that: " . . . there is a fundamental difference between probability and possibility". To explain this dif- ference he had given a special example illustrating the difference, which then was cited by many authors of books on Fuzzy Set The- ory and gained great importance for understanding the notion of possibility. In the paper the author presents his doubts as to this important example, explains why it is incorrect and gives a correct version of the example based on the notion of possibility distribution of Dubois and Prade.