 Whether or not we accept Levi’s convexity requirement, sets of probability functions give us the resources to distinguish ignorance from certainty about chances. If an agent is certain of an objective chance, every element of her credal committee will assign the same probability. However, if she is ignorant with respect to some proposition, her credal set will admit values in some interval \([a, b] \subseteq\) [0,1]. In her total ignorance about the ancient coin, Sophia might admit any value in the interval [0,1] for the proposition that it will land heads on the next spin. But since she knows that the Euro is fair, every member of her credal committee assigns .5 to the corresponding proposition. If we similarly redefine expected utility, then a bet on the Euro that costs $1 and pays out $2 if it lands heads has positive expected utility. But a similar bet on the ancient coin has expected utility ranging from -$1 to $2. This distinction allows for different attitudes towards the two bets.