– 11 – 0 . 9 × 150 , 000 = 135 , 000 . As we will discuss in § 4, the decline in received light produced by a transit can be balanced by the gravitational lensing produced by the white dwarf. While this may make it difficult or impossible to detect transits in some systems, lensing produces strong, distinctive signatures, including ati-transits, in others. We can derive a rough estimate of the fraction of Kepler targets that might be orbited by transiting white dwarfs by generating a population of stars, including both singles and binaries, and then considering the evolution of each system. We identify those that will become main sequence stars that are both (1) in a range of masses likely to be monitored by Kepler , and (2) orbited by white dwarfs. We then compute the probability that the white dwarf will transit during the time of Kepler monitoring. For short orbital periods, the probability is R ∗ /a , where R ∗ is the radius of the monitored star and a is the final orbital separation. For orbital periods longer than τ$_{monitor}$ , the duration of monitoring, we multiply by a factor of τ$_{monitor}$/P$_{orb}$. We assume that 40% of all stellar systems are singles, and that the remainder are of higher multiplicity. We use a Miller-Scalo IMF (Miller & Scalo 1979) to select the masses of all single stars, and to select the primary mass for all multiples. This has the effect of favoring low-mass stars, even though we generate the full mass spectrum. The only multiple systems we explicitly consider are binaries. We select the secondary mass as follows: M 2 = M $_{1}$× u 0 . $^{8}$, where u is a random number chosen from a uniform distribution in the range 0 − 1 . We then generate orbital separations, selecting uniformly in log space from separations as small as three times the radius of the primary, and as large as 10 4 AU. Primary stars will fill their Roche lobes at some point in their evolution if the orbital separation lies within roughly an AU. This range of separations encompasses a large fraction of all binaries. Roche-lobe filling will lead either to a common envelope phase or to stable mass transfer. While a large fraction of common envelopes may end in mergers, those binaries that survive will have small orbital separations and therefore high probability of yielding transits. When mass transfer is stable, the final separation may be somewhat larger than the initial separation, but most orbits are smaller than a few AU (see Figure 3). The paragraph above describes the key reason why transiting white dwarfs must be common: they are produced by a large fraction of all primordial binaries. We used a simple value to which we normalize can therefore be viewed as a sort of average. 3.1. Calculations