First i want to say there are a lot of questions related to this, but i couldn't find a similar case.
Suppose we have the typical problem where we need to compute the probability of pass a multiple-choice test. There are 8 questions with 5 options each, only one is correct. 4 of this questions are easy and the probability of do it well is $2/3$, the other 4 are hard and the probability of do it well is $1/5$. You can pass the test if answer correct at least 5 questions.
Im thinking in the binomial distribution here (from 5 to 8), but in this problem the probability of success is not the same for every question (like in similar problems). So maybe i should use the union of the probability of success for any type of answer (easy or hard), and then apply the binomial distribution.