Probability of assumption

I saw something about a puzzle that goes something like this: "I have two children and one is a boy, what is the probability that I have two boys?". Other than the fact that the English language is ambiguous , I dislike these kinds of problems because it does not deal with a controlled environment and becomes meaningless to apply something like: "What is the probability of A given B or stated in symbolic form P(A|B)." It devolves to what is assumed and implied in the statement. I could imagine that there has been a biological accident and only one family has survived and he has posed this riddle to his children to explain Bayes theorem. So there is only one family alive and they have two children, no Mom, and either two boys or one boy and one girl.

The probabilities is a finite countable set as it is 1 and thus the probability is 100% for which ever condition exists. What really interests me is how that situation might evolve as it seems a rather bad social framework akin to the Garden of Eden premise with one mother , husband, and only boys. Something odd happens, if one is to accept the premise.

To pose the problem as other than P(A|B) is not a riddle, it is a measure of how far one might reach to measure !B and whether A is within the set of Bs or !Bs. To B or not 2 bees that is the question.

Anyway, It does have something to do with quantum mechanics as it deals with probability distributions and that can become tricky if the scope is not well defined and in my opinion the scope is always infinite and so it becomes imperfectly determinant in all cases.

Here is another opencourseware reference for Oxford mathematics that has a well structured sequence of dependencies and looks like it might contain some interesting references.

Here is a reference relating to the improper use of Del Grad and Curl.∇ I am not the only one who finds that nomenclature and operator symbol overloading is problematic.

It seems to me that it is even more complex than the symbols and relationships suggest. Some of these things recur in sequences and do have physical analogs. By that I mean there are real world application and real measurable and significant effects that happen in the scope of the factorial expansion of interacting relationships. I never had names for these relationships and so there can be no confusion for me. It is when people attempt to communicate complex issues that the problem arises. The improper use of symbols only adds to the confusion generated in a collaborative environment. This is also true in programming and it can some times take 30 people to replace one skilled programmer. If naming conventions are not used it can be impossible to actually use and extend software even when the source is available. There was a case that involved Company A, who were one of the largest companies in the world and Company B that was also one of those. I was tasked to resolve the issue of sale of a very large software system and it had been purposely "poisoned" in this way. I cannot name the companies or the software as it would violate non-disclosure. I can however know that not only is it a source of confusion to inadvertently overload symbols, but that it is done in practice to make it impossible to use either without a key or in the case of indiviuals, without the key that exists in that person's mind.

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