  A new class of identical particles which may exhibit both Bose and Fermi
statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an
uncertainity may be either an intrinsic property of a particle or can be viewed
as an ``experimental uncertainity''. Statistical equivalence of such particles
and particles obeying parastatistics of infinite order is shown. Generalized
statistical distributions are derived and statistical and thermodynamical
properties of an ideal gas of the particles are investigated. The physical
nature of such particles and the implications of this investigation for the
statistics of extremal black holes are discussed.
