how to determine the probability the two signals are equivalent
The statistical test for whether two signals ("samples" in stats language) are equivalent ("are drawn from the same distribution") is a test like t-test (for normal variables), paired sample t-test (if these are two signals measured at the same times), Mann-Whitney U test, Wilcoxon rank-sum test, etc.

There are a few things that make it hard to give specific answer in your case.  I think when you say "matrix" you mean vector or perhaps time series.  And it is really unclear what you mean by "mix together" (add?) and by "bags".  Why mix them? Why draw randomly?  Can't you just  use a statistical test on the samples without mixing them?  

If you can edit the question to show actual formulas or better source code, you could get a better answer.