- #1
jack1234
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I have a question regarding one of the axiom for probability, which is p(<sample space>)=1.
I do not understand why p(<sample space>)=1 is an axiom instead of theorem, since I can prove it with the following argument:
Since sample space has been defined as the set of all possible outcomes, hence in any case, the sample set must occur, therefore the probability of the occurring of sample space is 100%, which follows that p(<sample space>)=1.
What is the problem with the argument?
I do not understand why p(<sample space>)=1 is an axiom instead of theorem, since I can prove it with the following argument:
Since sample space has been defined as the set of all possible outcomes, hence in any case, the sample set must occur, therefore the probability of the occurring of sample space is 100%, which follows that p(<sample space>)=1.
What is the problem with the argument?