Well firstly, only click the button once and once only since you have made two duplicate questions. Just saying. x)
As for your question, I think this only occurs in Black 2 and White 2 according to what I read:
In Black 2 and White 2 the odds of passing down the Nature of the parent holding an Everstone is now 100%. If both parents are holding an Everstone, the odds are 50/50 between each of the parents' Natures.
According to your tags you are playing those games' predecessors, Black and White. It's only 50% in those games. So, my answer is it's a 50% chance it will happen.
Okay, hope I helped. :)