Suppose you have two sample spaces [itex]\Omega_A[/itex] and [itex]\Omega_B[/itex]. First space contain two outcomes A and A', where A = [itex]\Omega_A[/itex] - A', i.e. the opposite outcomes.(adsbygoogle = window.adsbygoogle || []).push({});

Second space also contains two opposite outcomes B = [itex]\Omega_B[/itex] - B'.

Now, suppose that there are dependencies between A, A' and B, B' like below:

A [itex]\rightarrow[/itex] B'

A'[itex]\rightarrow[/itex] B v B' (logical alternative)

B [itex]\rightarrow[/itex] A'

B'[itex]\rightarrow[/itex] A v A' (logical alternative)

So, occurrence of non-negative (i.e. A or B) event excludes such (i.e. non negative) event in the other space. Occurrence of a negative event (A' or B') does not imply anything in the other space. So the two "logical alternative" implications could be in fact skipped:

A [itex]\rightarrow[/itex] B'

B [itex]\rightarrow[/itex] A'

My question:

- how to approach this?

- is this covered in some math topic?

Best Regards,

Greg

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# Dependencies between two probability sample spaces OmegaA, OmegaB

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