  In the measurement of atmospheric nu_e and nu_mu fluxes, the calculations of
the Super Kamiokande group for the distinction between muon-like and
electronlike events observed in the water Cerenkov detector have initially
assumed a misidentification probability of less than 1 % and later 2 % for the
sub-GeV range. In the multi-GeV range, they compared only the observed
behaviors of ring patterns of muon and electron events, and claimed a 3 %
mis-identification. However, the expressions and the calculation method do not
include the fluctuation properties due to the stochastic nature of the
processes which determine the expected number of photoelectrons (p.e.) produced
by muons and electrons. Our full Monte Carlo (MC) simulations including the
fluctuations of photoelectron production show that the total mis-identification
rate for electrons and muons should be larger than or equal to 20 % for sub-GeV
region. Even in the multi-GeV region we expect a mis-identification rate of
several % based on our MC simulations taking into account the ring patterns.
The mis-identified events are mostly of muonic origin.
