  A fundamental issue for any quantum cosmological theory is to specify how
probabilities can be assigned to various quantum events or sequences of events
such as the occurrence of singularities or bounces. In previous work, we have
demonstrated how this issue can be successfully addressed within the consistent
histories approach to quantum theory for Wheeler-DeWitt-quantized cosmological
models. In this work, we generalize that analysis to the exactly solvable loop
quantization of a spatially flat, homogeneous and isotropic cosmology sourced
with a massless, minimally coupled scalar field known as sLQC. We provide an
explicit, rigorous and complete decoherent histories formulation for this model
and compute the probabilities for the occurrence of a quantum bounce vs. a
singularity. Using the scalar field as an emergent internal time, we show for
generic states that the probability for a singularity to occur in this model is
zero, and that of a bounce is unity, complementing earlier studies of the
expectation values of the volume and matter density in this theory. We also
show from the consistent histories point of view that all states in this model,
whether quantum or classical, achieve arbitrarily large volume in the limit of
infinite `past' or `future' scalar `time', in the sense that the wave function
evaluated at any arbitrary fixed value of the volume vanishes in that limit.
Finally, we briefly discuss certain misconceptions concerning the utility of
the consistent histories approach in these models.
