Estimate the probability of all RVs to be in the given percentile

[PavelRechkalov]

Is there a way to estimate the probability of all RVs to be in the given percentile (given their joint probability distribution based on the given copula)?

E.g., assume I have 3 RVs. I link their marginal w/ whatever copula. Then, I'd like to know what's the probability that all 3 RVs jointly happen to draw a value in 10% percentile?

Regards