Ordinal optimization concentrates on finding a subset of good designs, by approximately evaluating a parallel set of designs, and reduces the required simulation time dramatically for discrete-event simulation and optimization, The estimation of the confidence probability (CP) that the selected designs contain at least one good design is crucial to ordinal optimization. However, it is very difficult to estimate this probability in DES simulation, especially for complicated DES with large number of designs, This paper proposes two simple lower bounds for quantifying the confidence probability. Numerical testing will be presented.