It is my understanding that most VCs expect only one in ten businesses to succeed, but that one is enough to offset the loss and ensure a profit.

This is correct. For small and medium funds, a single successful portfolio company can return their entire fund with some multiple on top of this. The reason you invest in 30-40 companies instead of one is because you don't know which one it'll be.

I've seen this from the inside, I liked the company a lot but I'd never suspect it'd become the most obvious success for us.