Using a comprehensive binary population synthesis scheme, we investigate the statistical properties of a sample of eclipsing binaries that is detectable by an idealised extrasolar planet transit survey with specifications broadly similar to those of the SuperWASP (Wide Angle Search for Planets) project. In this idealised survey the total number of detectable single stars in the Galactic disc is of the order of 10^6-10^7, while, for a flat initial mass ratio distribution, the total number of detectable eclipsing binaries is of the order of 10^4-10^5. The majority of the population of detectable single stars is made up of main-sequence stars (60%), horizontal-branch stars (20%), and giant-branch stars (10%). The largest contributions to the population of detectable eclipsing binaries stem from detached double main-sequence star binaries (60%), detached giant-branch main-sequence star binaries (20%), and detached horizontal-branch main-sequence star binaries (10%). The ratio of the number of eclipsing binaries to the number of single stars detectable by the idealised SuperWASP survey varies by less than a factor of 2.5 across the sky, and decreases with increasing Galactic latitude. It is found to be largest in the direction of the Galactic longitude l=-7.5deg and the Galactic latitude b=-22.5deg. We also show that the fractions of systems in different subgroups of eclipsing binaries are sensitive to the adopted initial mass ratio distribution, which is one of the poorest constrained input parameters in present-day binary population synthesis calculations. This suggests that once statistically meaningful results from transit surveys are available, they will be able to significantly improve the predictive power of population synthesis studies of interacting binaries and related objects. (abridged)
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