Consider three events: $E_1$, $E_2$ and $E_3$. They are neither mutually exclusive nor independent. Let's say that the correlation coefficient between $E_i$ and $E_j$ is given by $\rho_{ij}$. Let's also assume that the probability of $E_i$ occurring is $P(E_i)$.
How do we calculate the probability that at least one of these three events occurs? Any references that develop a general methodology to calculate probabilities when events share these two characteristics (mutually non-exclusive and correlated)?
Any help much appreciated! Thanks in advance.