Number of hits can vary a great deal. I was doing a quest for the shrine of Azura, putting down a couple of her supporters who had unwillingly turned into vampires, and I didn't check my active effects when I came out. After three days of more adventure, it turns out I'm a vampire

Just shows it can happen totally unexpectedly, although I was slightly naive as to expect not to get anything from the vampires.
I hadn't been planning on that, and I got a cure as quickly as possible, leaving as little pin-pricks in peoples' necks as possible

Vampirism can be a very big pain in the neck (excuse the very bad pun here -

) if you're not prepared for it.