Thank you Peter Gotch for your kindness in answering my concerns so extensively.
You'll be right that I haven't explained myself well. For that reason I received answers that I did not expect from my question. Perhaps the reason is because my question is formulated in an abstract way, because it does not ask for an answer to solve a practical problem, but to solve a theoretical problem. And the people who go to these forums generally do so to ask for help to solve a practical problem in the exercise of their profession. For this reason the answers tend to give concrete examples, when what I request is an imaginary dialogue with a person interested in occupational hazards. The comments of my imaginary interlocutor are the kind of answers I expect. I think that will explain me better.
amungar: John, I have doubts about the effectiveness of the traditional formula for assessing occupational hazards in a given job: "risk = probability of (certain) accident x severity of its consequences". The reason is because the mathematical concept "probability" is applicable to a set of homogeneous events, where we want to know what the frequency of a given event is. Consequently, this formula is inapplicable to a given job because the frequency of the “accident” event is the constant ½, the result of the ratio between the favorable case “accident” and the two possible cases “true accident and false accident”. What do you think?
John: amungar, I think that for a given job the probability of accident should not be interpreted in a mathematical sense, but rather subjective, because the purpose is to estimate the ease of accident occurrence by applying intuition.
amungar: I understand you very well John, but then this formula should use the expression "accident facility" or, better yet, the expression "possibility of accident". But experience tells us that the magnitude of the possibility of an accident depends on the danger. In this case, if we substitute the imprecise concept “possibility of an accident” with the more precise concept “danger”, an inconsistency appears, because risk and danger are similar concepts, which now is not the case to go into detail to distinguish them. What do you think?
John: amungar, you have put me in a hurry because what you say is reasonable. I realize that the concept “danger” that, with very good criteria you have introduced, implicitly indicates that it would be necessary to replace the concepts “accident probability”, “possibility of accident” and “danger” by the concept of “insecurity in the work” because, at the end of the case, the presence of insecurity is the cause that facilitates the accident. Naturally, I do not mean any insecurity, but rather a certain insecurity that facilitates the occurrence of a certain accident.
amungar: John, I see that you have perfectly understood my doubt about that famous formula and, even, you have gone further because you have been able to understand the root of the problem. I agree with you that it would be convenient to replace the concept “probability of (certain) accident” with the concept “insecurity that facilitates the occurrence of a certain accident”. Congratulations!
What is your opinion of this imaginary conversation?
NOTE: I apologize if there is any inconsistency in the text because it is an English translation using the Google translator.