Given a list of $i$ probability distributions $f_j(x)$ and a list of $i$ probabilities $p_j$ and an interval I.
A probability distribution $f_z(x)$ is chosen from the list with probability p_z and a random number R from the interval I is chosen with this distribution.
Given $R$,$I$ and the two lists of distributions and associated probabilities, how to find the probability that the distribution with an index of $n$ was chosen?