What's wrong with Randi starting her own business(es)? Just because she is leaving Facebook to start her own stuff doesn't mean that whatever she starts will compete with Facebook.
in corporate world, it's not about competing only. it's more to who came up with an idea that sells. e.g. if any of Randi's idea was deemed to have been thought up while still in Facebook, then Facebook will lay claim to it as their collective idea and will contest it. just like the idea of "facebook" was contested a few years back by Zuckerberg's former classmates/associates.
but then who knows, Big Z might play the benevolent brother and let the sister's company prosper. only to buyout later if it's successful.