  Recently a new model with hidden variables of the wave type was elaborated,
so called prequantum classical statistical field theory (PCSFT). Roughly
speaking PCSFT is a classical signal theory applied to a special class of
signals -- "quantum systems". PCSFT reproduces successfully all probabilistic
predictions of QM, including correlations for entangled systems. This model
peacefully coexists with all known no-go theorems, including Bell's theorem. In
our approach QM is an approximate model. All probabilistic predictions of QM
are only (quite good) approximations of "real physical averages". The latter
are averages with respect to fluctuations of prequantum fields. In particular,
Born's rule is only an approximate rule. More precise experiments should
demonstrate its violation. We present a simple experiment which has to produce
statistical data violating Born's rule. Since the PCSFT-presentation of this
experiment may be difficult for experimenters, we reformulate consequences of
PCSFT in terms of the conventional wave function. In general, deviation from
Born's rule is rather small. We found an experiment amplifying this deviation.
We start with a toy example in section 2. Then we present a more realistic
example based on Gaussian states with very small dispersion, see section 3.
