Thread: Probability and Stochastic Processes

I have 5 questions. I want to answer them with quality and good sentences.

Question-a)Are events A and A^c mutually exclusive? Given two mutually exclusive events A and B, is it always true that B=A^c ?

Question-b) Is it reasonable to use traditional definition to find the probability that a particular face of unfair die will show up?

Question-c) Can we use the three axioms of probability alone to find the probability of an event?

Question-d) Are P(AB) and P(A,B) different notations of the same thing?

Question-e) Under what condition for the set of events A1,A2 ,…..,An can total probability theorem be applied to event B?

Q1: Mutually exclusive typically means that the event sets are disjoint. So yes to first part and no to second.
Q2: Don't understand question?
Q3: No (think about it)
Q4: Depends on what A and B are
Q5: Pairwise disjointness?

no other information for all of questions