This paper reports the design and optimization of a double-stranded molecular probe for homogeneous detection of specific nucleotide sequences. The probes are labeled with either a fluorophore or a quencher such that the probe hybridization brings the two labels into close proximity, and this diminishes the fluorescence signal in the absence of a target. In the presence of a target, the fluorophore probe is thermodynamically driven to unzip from its hybridized form and bind with the target. An equilibrium analysis, which successfully describes all the major features of the assay without any fitting parameter, is performed to generalize the design of the probe. Several key parameters affecting the performance of the assay are examined. We show that the dynamic range and the signal-to-noise ratio of the assay can be optimized by the probe concentration, the quencher-to-fluorophore ratio, and the probe strand sequence. By proper design of the sequence, the probe discriminates single nucleotide mismatches in a single step without any separation step or measurement of melting profile.