There are different kinds of ignorance. There is, on the one hand, the kind of ignorance exemplified by someone who knows there are exactly 50 red and 50 blue balls in an urn, but doesn’t know whether a red or a blue ball will be drawn from it. Then there is the kind of ignorance exemplified by someone who only knows there are 100 balls in the urn, each of which is either red or blue, but doesn’t know in what proportions. On pain of conflating these two epistemic states, the latter shouldn’t be represented with the same kind of measure as the former. The key to solving the Sleeping Beauty problem is to find a reasonable representation of Beauty’s ignorance with regard to it being Monday or Tuesday when she wakes up. On any ordinary probability assignment, Beauty’s credence in heads should be less than 1/2. But using an ordinary probability assignment would be to misrepresent Beauty’s epistemic state. By applying the Dempster-Shafer theory of non-additive degrees of belief to the Sleeping Beauty problem, we get an argument in favor of the 1/2 solution.