Probabilistic equivalence is a concept in experimental design methodology, which implies that the researcher is perfectly aware of the odds that he or she will find come across a pretest difference between the two groups under investigation. However, it does not necessarily mean that the two groups being studied will have similar pretest means.
In as much as one is likely to observe pretest differences, these must likely be due to chance since it is only by chance that the researcher accessed the groups out of the wider population. Therefore, pretest differences do not have any implications on the posttest.
Probabilistic equivalence is important because it helps to eradicate prejudice in experiments. Since researchers are likely to encounter pretest differences, probabilistic equivalence states that this is only due to probability and will not have any impact on the final tests on the two groups. Therefore, there can be no need of bringing in prejudices after the pretests, since these results are only based on chance.