 Popular discourse often takes hope to be synonymous with optimism. But while optimism can be usefully analyzed as a desire for an outcome together with a belief that the outcome is more likely than not (or more likely than the evidence leads other people to believe), many philosophers hold that hope, properly understood, is independent of probability assessments (see  section 3).  One can hope for outcomes that one considers to be very unlikely and that one does not expect to happen, such as a miraculous cure of an illness. In such cases, optimism is not an appropriate response.