  We present a measurement of the ttbar production cross section using events
with one charged lepton and jets from ppbar collisions at a center-of-mass
energy of 1.96 TeV. A b-tagging algorithm based on the probability of displaced
tracks coming from the event interaction vertex is applied to identify b quarks
from top decay. Using 318 pb^{-1} of data collected with the CDF II detector,
we measure the ttbar production cross section in events with at least one
restrictive (tight) b-tagged jet and obtain 8.9 +1.0-1.0 (stat.) +1.1-1.0
(syst.) pb. The cross section value assumes a top quark mass of m_{t}=178 GeV
in the acceptance corrections. The dependence of the cross section on m_t is
presented in the paper. This result is consistent with other CDF measurements
of the ttbar cross section using different samples and analysis techniques, and
has similar systematic uncertainties. We have also performed consistency checks
by using the b-tagging probability function to vary the signal to background
ratio and also using events that have at least two b-tagged jets.
