Astrophysical false positives due to stellar eclipsing binaries pose one of the greatest challenges to ground-based surveys for transiting Hot Jupiters. We have used known properties of multiple star systems and Hot Jupiter systems to predict, a priori, the number of such false detections and the number of genuine planet detections recovered in two hypothetical but realistic ground-based transit surveys targeting fields close to the galactic plane (b~10 degrees): a shallow survey covering a magnitude range 10<V<13, and a deep survey covering a magnitude range 15<V<19. Our results are consistent with the commonly-reported experience of false detections outnumbering planet detections by a factor of ~10 in shallow surveys, while in our synthetic deep survey we find ~1-2 false detections for every planet detection. We characterize the eclipsing binary configurations that are most likely to cause false detections and find that they can be divided into three main types: (i) two dwarfs undergoing grazing transits, (ii) two dwarfs undergoing low-latitude transits in which one component has a substantially smaller radius than the other, and (iii) two eclipsing dwarfs blended with one or more physically unassociated foreground stars. We also predict that a significant fraction of Hot Jupiter detections are blended with the light from other stars, showing that care must be taken to identify the presence of any unresolved neighbors in order to obtain accurate estimates of planetary radii. This issue is likely to extend to terrestrial planet candidates in the CoRoT and Kepler transit surveys, for which neighbors of much fainter relative brightness will be important.
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