  Observationally, fast radio bursts (FRBs) can be divided into repeating and
apparently non-repeating (one-off) ones. It is unclear whether all FRBs repeat
and whether there are genuine non-repeating FRBs. We attempt to address these
questions using Monte Carlo simulations. We define a parameter $T_c$ at which
the accumulated number of non-repeating sources becomes comparable to the total
number of the repeating sources, which is a good proxy to denote the intrinsic
repeater fraction among FRBs. Assuming that both types of sources exist and
that their burst energies follow power law distributions, we investigate how
the {\em observed} repeater fraction evolves with time for different
parameters. If the lifetime of repeaters is sufficiently long so that the
evolutionary effect can be neglected within the observational time span, unless
$T_c \rightarrow \infty$ (i.e. there is no genuine non-repeating FRB source)
the observed repeater fraction should increase with time first, reach a peak,
and then decline. The peak time $T_p$ and the peak fraction $F_{\rm r,obs,p}$
depend on $T_c$ and other repeating rate parameters. With the current data, we
pose a lower limit $T_c > 0.1$ d for reasonable parameter values. We predict
that future continuous monitoring of FRBs with CHIME or similar wide-field
radio telescopes would obtain an $F_{\rm r,obs}$ less than $0.04$. The
detection of a smaller peak value $F_{\rm r,obs,p}<0.04$ in the near future
would disfavor the ansatz that "all FRB sources repeat".
