I'm struggling with establishing proper equation for calculating probability of occurrence N events (correlated with each other or not) in the list. I spent more than a month on it and can't find the proper one.
I have N events with probability of occurrence for every of them. For example:
- ()= 0.42
- ()= 0.42
- (C)= 0.52
I also have correlation matrix (Pearson Correlation) of those events, for example:
- = 0
- = 0.5
- = 0.5
All events in the list might be independent (correlation = 0) and dependent (correlation != 0) as well. Although those events will never be mutually exclusive or complementary.
I would like to find an equation which result will be equal to final probability of occurrence of all those events at once given the fact that if event A or B occurs then the event C is much more likely to happen.
For now I have tried to adapt the result from this thread Probability of three events occurring given correlation? but it came out that it's harder than I thought as in the thread it's a 1-dimensional problem but in this case we have 2-dimensional.
It would be great if you'd help me with the equation or some suggestions/tips on how to tackle the problem (maybe there is other way) because I think I'm missing something here.
Thanks in advance for help!