Dependencies between two probability sample spaces OmegaA, OmegaB

[Grag]

Suppose you have two sample spaces $\Omega_A$ and $\Omega_B$. First space contain two outcomes A and A', where A = $\Omega_A$ - A', i.e. the opposite outcomes.

Second space also contains two opposite outcomes B = $\Omega_B$ - B'.

Now, suppose that there are dependencies between A, A' and B, B' like below:
A $\rightarrow$ B'
A'$\rightarrow$ B v B' (logical alternative)
B $\rightarrow$ A'
B'$\rightarrow$ 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 $\rightarrow$ B'
B $\rightarrow$ A'


My question:
- how to approach this?
- is this covered in some math topic?

Best Regards,
Greg

 

[Valkarie]

orThis type of problem is often studied in the field of probability theory. The concept of conditional probability can help you understand the relationships between the two events, and how they affect each other. The conditional probability of event A given event B is the probability that A occurs given that B has already occurred. You can also calculate the probability of both events occurring together, which is known as the joint probability. With these tools, you can analyze how the different events interact with each other and how their probabilities are affected by one another.