There seems to be nothing short of a {\it double whammy} hitting the users of probability, and among them physicists, especially those involved in the foundations of quanta. First is the instant instinctual reaction that phenomena which interest one do sharply and clearly divide into the {\it dichotomy} of {\it two and only two} alternatives of being {\it either} ``deterministic", {\it or} on the contrary, being ``probabilistic". However, there is also a second, prior and yet deeper trouble, namely, the ``probabilistic" case is strongly believed to be equally clear and well-founded as is the ``deterministic" one. And the only difference seen between the two is that the latter can talk also about ``individual" phenomena, while the former can only do so about large enough ``ensembles" for which, however, it is believed to be equally clear, precise and rigorous with the ``deterministic" approach. Or briefly, ``probabilistic'' is seen as nothing else but the ``deterministic'' on the level of ``ensembles" ... \\ The fact, however, is that there is a {\it deep gap} between the empirical world of ``random" phenomena, and on the other hand, theories of ``probability". Furthermore, any attempt to bridge that gap does inevitably involve {\it infinity}, thus aggravating the situation to the extent that even today, and even if not quite realized by many, theories of ``probabilities" have a {\it shaky} foundation. \\ This paper tries to bring to the awareness of various users of ``probabilities", and among them, to physicists involved in quanta, the fact that - seemingly unknown to them - they are self-inflicted victims of the mentioned double whammy.