The apparent contact angle on a rough surface is usually modeled by either Cassie's or Wenzel's theory. We show, on the basis of experimental evidence, that there can be two contact angles on the same rough surface, depending on how a drop is formed. A transition can occur between the different states by an external disturbance. This paper compares the theoretical prediction with matching experiments. This leads to the establishment of a design criterion for a robust hydrophobic rough surface on which the apparent contact angle will not change as a result of an external disturbance.