  Transits on single stars are rare. The probability rarely exceeds a few per
cent. Furthermore, this probability rapidly approaches zero at increasing
orbital period. Therefore transit surveys have been predominantly limited to
the inner parts of exoplanetary systems. Here we demonstrate how circumbinary
planets allow us to beat these unfavourable odds. By incorporating the geometry
and the three-body dynamics of circumbinary systems, we analytically derive the
probability of transitability, a configuration where the binary and planet
orbits overlap on the sky. We later show that this is equivalent to the transit
probability, but at an unspecified point in time. This probability, at its
minimum, is always higher than for single star cases. In addition, it is an
increasing function with mutual inclination. By applying our analytical
development to eclipsing binaries, we deduce that transits are highly probable,
and in some case guaranteed. For example, a circumbinary planet revolving at 1
AU around a 0.3 AU eclipsing binary is certain to eventually transit - a 100%
probability - if its mutual inclination is greater than 0.6 deg. We show that
the transit probability is generally only a weak function of the planet's
orbital period; circumbinary planets may be used as practical tools for probing
the outer regions of exoplanetary systems to search for and detect warm to cold
transiting planets.
