  Gamma-Ray Bursts (GRBs) are traditionally divided to long and short according
to their durations (>/< 2 sec). It was generally believed that this reflects a
different physical origin: Collapsars (long) and non-Collapsars (short). We
have recently shown that the duration distribution of Collapsars is flat,
namely independent of the duration, at short durations. Using this model for
the distribution of Collapsars we determine the duration distribution of
non-Collapsars and estimate the probability that a burst with a given duration
(and hardness) is a Collapsar or not. We find that this probability depends
strongly on the spectral window of the observing detector. While the commonly
used limit of 2 sec is conservative and suitable for BATSE bursts, 40% of
swift's bursts shorter than 2 sec are Collapsars and division >/<0.8 sec is
more suitable for swift. We find that the duration overlap of the two
populations is very large. On the one hand there is a non-negligible fraction
of non-Collapsars longer than 10 sec, while on the other hand even bursts
shorter than 0.5 sec in the swift sample have a non-negligible probability to
be Collapsars. Our results enable the construction of non-Collapsar samples
while controlling the Collapsar contamination. They also highlight that no firm
conclusions can be drawn based on a single burst and they have numerous
implications concerning previous studies of non-Collapsar properties that were
based on the current significantly contaminated swift samples of localized
short GRBs. Specifically: (i) all known short bursts with z>1 are most likely
Collapsars, (ii) the only short burst with a clear jet break is most likely a
Collapsar, indicating our lack of knowledge concerning non-Collapsar beaming
(iii) the existence of non-Collapsars with durations up to 10 sec impose new
challenges to non-Collapsar models.
