Launching a starshade to rendezvous with the Nancy Grace Roman Space Telescope (Roman) would provide the first opportunity to directly image the habitable zones (HZs) of nearby sunlike stars in the coming decade. A report on the science and feasibility of such a mission was recently submitted to NASA as a probe study concept. The driving objective of the concept is to determine whether Earth-like exoplanets exist in the HZs of the nearest sunlike stars and have biosignature gases in their atmospheres. With the sensitivity provided by this telescope, it is possible to measure the brightness of zodiacal dust disks around the nearest sunlike stars and establish how their population compares with our own. In addition, known gas-giant exoplanets can be targeted to measure their atmospheric metallicity and thereby determine if the correlation with planet mass follows the trend observed in the Solar System and hinted at by exoplanet transit spectroscopy data. We provide the details of the calculations used to estimate the sensitivity of Roman with a starshade and describe the publicly available Python-based source code used to make these calculations. Given the fixed capability of Roman and the constrained observing windows inherent for the starshade, we calculate the sensitivity of the combined observatory to detect these three types of targets, and we present an overall observing strategy that enables us to achieve these objectives.