Expected Value for Intersection of Subset Sets in a Set?

AI Thread Summary
The discussion focuses on calculating the expected value for the intersection of two subsets A and B from a set X with n elements. It highlights the complexity of determining the intersection's expected value, particularly when considering all possible combinations of A and B. For n=3, there are 64 different selections for the intersection, making the calculation intricate. Participants express uncertainty about defining the expected value in non-numeric outcomes and seek a more straightforward approach to the problem. Overall, the conversation emphasizes the challenges in deriving a general formula for expected value in this context.
sylar
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Let X be a set with n elements, and let A,B be subsets of X. What is the general expected value for the intersection of these two sets?

Here for each n, we must find the possibility of having an intersection set of elements, multiply this probability by n, and then sum up the products we obtained.

Take the case when n=3. Then there are 8 different possibilities for choosing A, and also for B. Thus, there are 64 different possible selections of A int. B. We must find the possibility of having the set A int. B with n elements, where n=0,1,2,3, and this seems very complicated. So, is there a better approach for this (general) problem? Thanks!
 
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"Expected value" is normally a number. It is not at all clear to me how you would define the "expected value" when the outcomes are not themselves numeric.
 

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