Abridged… Blue stragglers (BSS) are thought to be the product of either primordial or collisional binary systems. In the context of dwarf spheroidal galaxies it is hard to firmly disentangle a genuine BSS population from young main sequence (MS) stars tracing a ~1-2 Gyr old star forming episode. Assuming that their blue plume populations are made of BSS, we estimate the BSS frequency for 8 Local Group non star-forming dwarf galaxies, using a compilation of ground and space based photometry. Our results can be summarized as follows: (i) The BSS frequency in dwarf galaxies, at any given Mv, is always higher than that in globular clusters of similar luminosities; (ii) the BSS frequency for the lowest luminosity dwarf galaxies is in excellent agreement with that observed in the Milky Way halo; and most interestingly (iii) derive a statistically significant anti-correlation between the BSS frequency and the galaxy Mv. The low density, almost collision-less, environments of our dwarf galaxy sample allow us to infer (i) their very low dynamical evolution; (ii) a negligible production of collisional BSS; and consequently (iii) that their blue plumes are mainly made of primordial binaries. The dwarf galaxies anti-correlation can be used as a discriminator: galaxies obeying the anti-correlation are more likely to possess genuine primordial BSS rather than young main sequence stars.

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