I am a freshman here with the following question, sorry for my gramar I don't know the exact matematical probability terms in english.
So, if I have a sample space, can I define in this space 2 probability?
I know that, the probability function fit 3 condition.
- $P(a) \ge 0$
- $P(\Omega) = 1$
- $P\left(\bigcup_{j\in J}A_j\right) =\sum_{j\in J}P(A_j)$
The following probabilities function fit the conditions: probability as geometrie, probability as counting, probability as algebra. Example: probability as counting P(event) = of successful outcomes / of total outcomes
So can I define a 2 function on the same sample space? If not why, how to prove it? If anyone can give me examples, I would be very grateful.
I want to understand this with 100% percent.
Thank you very much.