Hi,
I am faced with following case and would very gratefully need advice about
the correctness of my judgment.
I have 2 sets of events. A1, A2, A3 (disjoint) and B1, B2, B3 (disjoint)
where the sum of the probabilities of the A events is 1 and those of the B
events are one. Sum P(Ai)=1 and Sum P(Bi)=1, where i=1,2,3
The A and B events jointly occur where P(Ai,Bj)=P(Ai)*P(Bj).
Case 1: Occurs when all possible joining of A events and B events can occur,
hence the sum of probabilities of all joint events is 1 (Sum P(Ai,Bj)=1).
i=1,2,3 and j=1,2,3
Case 2: there has been some constraints that prevent certain joining of
events. Say (A2 and B3), and (A1 and B1) cannot occur simultaneously. Now
the Sum P(Ai,Bj)=1), for all possible joining, is less than 1.
What I would like to do is to compare some probabilities in two situations,
one based on Case 1 and the other on Case 2. However, Case 2 sample space
has a probability of less than 1, and the probabilities in the situation
based on Case 2 will be less than those based on Case 1.
Will it be correct to normalize the joint probabilities in Case 2 so that
they add up to 1 then compare them to those in the situation based on Case
1?
Can someone please advise me about this?
Best Regards
Etienne
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