Looking for a simple random biased method to order a set

I am looking for a sampling method with the following característics :

1) I will divide the sampling set in two main groups. The members belonging to one of the those two groups will have a greater probability of being sampled than the members of the other group.

2) A specific criterial will direct the probability of any member of the main set (regardless of the subgroups described in 1) being sampled, but the wheight of this criteria in the sampling probability should be less strong than the criteria described in 1)

Can someone help me with that ? Thanks in advance.


Omega Contributor
I don't follow what you are trying to do. Sample a set with a higher probability of being sampled? Please provide a little more information. Thank you.