Basic Question

#1
Hi all,

I feel a little embarrassed about this, but: what is the rule linking the probability of an event A to the weighted sum of its sub-events? E.g. if A is a set of three events, {a1, a2, a3}, then P(A) = E(a*), right? Is it derivable from the axioms? Does this rule have a name? Thank you!
 

Dason

Ambassador to the humans
#2
P(A) = E(a*) doesn't really make sense to me. The expected value of an event isn't a well-defined quantity in general. Can you try to explain what you mean again?
 
#3
Yes. The original statement was muddled. The equation in question: P(A) = P(a1 or a2 or a3) where A = {a1, a2, a3}. Is there anything that needs to be said in justifying this equation? Like equal measures on identical sets? Is there a standard terminology for this kind of situation?