Probability of three events occurring given correlation?
Solution 1:
As I found out in this presentation, where the above-mentioned issue is dealt with in the context of default correlations, the problem is not possible to be solved with the inputs given.
I.e., when 3 events have defined probabilities of happening, the pairwise correlations are not enough to construct the joint probability of all 3 events happening.
In the context of default correlations, complex problems of correlations of events are solved using other methods such as Copula functions.