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Sequence E variables are close binary red giants that show ellipsoidal light variations. They are likely the immediate precursors of planetary nebulae (PNe) with close binary central stars as well as other binary post‐asymptotic giant branch (post‐AGB) and binary post‐red giant branch (post‐RGB) stars. We have made a Monte Carlo simulation to determine the fraction of red giant binaries that go through a common envelope event leading to the production of a close binary system or a merged star. The novel aspect of this simulation is that we use the observed frequency of sequence E binaries in the Large Magellanic Cloud (LMC) to normalize our calculations. This normalization allows us to produce predictions that are relatively independent of model assumptions. In our standard model, and assuming that the relative numbers of PNe of various types are proportional to their birth rates, we find that in the LMC today the fraction of PNe with close binary central stars is 7–9 per cent, the fraction of PNe with intermediate period binary central stars having separations capable of influencing the nebula shape (orbital periods less than 500 yr) is 23–27 per cent, the fraction of PNe containing wide binaries that are unable to influence the nebula shape (orbital period greater than 500 yr) is 46–55 per cent, the fraction of PNe derived from single stars is 3–19 per cent, and 5–6 per cent of PNe are produced by previously merged stars. We also predict that the birth rate of post‐RGB stars is ∼4 per cent of the total PN birth rate, equivalent to ∼50 per cent of the production rate of PNe with close binary central stars. These post‐RGB stars most likely appear initially as luminous low‐mass helium white dwarf binaries. The average lifetime of sequence E ellipsoidal variability with amplitude more than 0.02 mag is predicted to be ∼0.95 Myr. We use our model and the observed number of red giant stars in the top one magnitude of the RGB in the LMC to predict the number of PNe in the LMC. We predict 548 PNe in good agreement with the 541 ± 89 PNe observed by Reid &amp; Parker. Since most of these PNe come from single or non‐interacting binary stars in our model, this means that most such stars produce PNe contrary to the ‘binary hypothesis’ which suggests that binary interaction is required to produce a PN.

Predicting the fate of binary red giants using the observed sequence E star population: binary planetary nebula nuclei and post‐RGB stars