This thesis documents the measurement of the $t\bar t$ production cross section using events with one charged lepton and jets from $p\bar p$ 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~$\ipb$ of data collected with the {\CDFII} detector, we measure the $t\bar t$ 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 a\-ssu\-mes a top quark mass of $m_{t}=178~\Gevcc$ 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 $t\bar t$ 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. Posted to /cdf/pub/thesis/cdf8772_ttbar_xsect_jetprob.ps http://www-cdf.fnal.gov/thesis/cdf8772_ttbar_xsect_jetprob.ps Posted by palencia