Proposal for an explanation of established law

Hello Rabbi,
Following your last class in Ra’anana on the majority in Halacha and in general, I thought of an explanation for the fixed law (which may have been included in your words in the class):
When a person or even an animal like a mouse chooses an item of a certain type from a mixture of items, the chance that he chose an item of a certain type depends not on the relative quantity of items of that particular type but on the voter’s preference considerations. For example, if a person throws a stone at a group of people with a majority of Jews and a minority of Gentiles, the chance that he meant a Gentile and not a Jew is 50% because it is a question of intention, and his intention is unknown to us, and therefore in the absence of information we assume that he meant either a Gentile or a Jew with equal probability. In the same way, if a mouse takes a loaf from 9 matzah clusters and 1 chametz, there is a 50/50 chance of which type of loaf it will choose because it depends on its preferences, and not on the public majority or minority of matzah. Even in 9 stores, if a person entered a store and took meat from there and then forgot which store he entered, the question is where he intended to enter when he went to buy the meat, and this is a question that has two possible answers (to enter a kosher or a rabbi store) with equal probabilities, and this has nothing to do with the number of kosher or rabbi stores. But if the piece separated on its own, without any selective process being involved (for example, it fell off a transportation cart), in such a case one must go after most of the stores, because the chance that the piece will separate on its own is equal for every store. In other words, the explanation for the fixed law is what symmetry assumption is made, between the different qualities (kosher/rabbi, chametz/matza, gentile/Jewish) or between the different quantities (9 kosher/1 rabbi, 9 matza/1 chametz, 9 Jews, 1 gentile). In any case, one must exercise judgment as to what symmetry is appropriate for the case in question. For example, you gave an example of 9 blue balls and 1 red ball, what is the chance that a person will draw a red ball from the mixture, and you said that the chance is actually 50% and not 10% because it depends on the person’s preferences.
What do you think?
Best regards,