How do you get a set of {2 ... 24} for throwing the same number of dice?
You can only get 2 by throwing one or two dice. You can only get 24 by throwing between 4 and 24 dice.
Student or Learner
How would you define the difference between them?
I will tell you mine using my own ideas and words:
We can describe present, past, and future events by expressing our degree of inclination to believe they are happening, happened, or will happen; and this is when these two words are addressed.
Before we issue our description, we will use our intuitive and subjective judgment and assume with good cause that something is "left" or "right".
Possibility. To me it says whether the happening of something, given the circuimstances, contradicts something else, thus incapable to exist in fact, unrealizable. Let me give you an example. Dice. Mathematicians like dice. We have two dice. Six sides to each and six different numbers of dots, as one would expect upon conventions. Before I throw them I ask myself the question: "Would it go against anything if I threw 13 or 1.3?" "Yes!" And after careful considerations, I say, according to my definition of possible: "No, it is not possible that I throw these numbers, because 13, 1.3 ∉ 12≥ (x+y)∈N ≥ 2"
What does probabilty mean in the case of our dice-throwing? What are all the possible (now that we know what possible means we can use it) outcomes?
O = {2; ... ; 24 }; n∈N
The probability of throwing 2 or 24 is very low.
The probabilty of throwing 12 is relatively strong.
When we talk about probability, we do not only say something is possible, but we also say how possible. Very, perfectly, just, theoretically, 60%, 12%, etc.
The question rightfully arises, what do possibility and probability mean modality-wise?
He may/might/can/could be at home. -- possible but not probable, because we are too uncertain to be able to grade the possibity.
He can't be at home. -- the probability of him being at home is zero, in my opinion. It is beyond (my) reasonable doubt.
He must be at home. -- in all probabilty
He is at home -- in all probability
He should/will be at home -- What is this? prob or pos?
He has to be at home by now. -- prob?
What do you think?
How do you get a set of {2 ... 24} for throwing the same number of dice?
You can only get 2 by throwing one or two dice. You can only get 24 by throwing between 4 and 24 dice.
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