  Full counting statistics is a powerful tool to characterize the noise and
correlations in transport through mesoscopic systems. In this work, we propose
the theory of conditional spin counting statistics, i.e., the statistical
fluctuations of spin-up (down) current given the observation of the spin-down
(up) current. In the context of transport through a single quantum dot, it is
demonstrated that a strong Coulomb interaction leads to a conditional spin
counting statistics that exhibits a substantial change in comparison to that
without Coulomb repulsion. It thus can be served as an effective way to probe
the Coulomb interactions in mesoscopic transport systems. In case of spin
polarized transport, it is further shown that the conditional spin counting
statistics offers a transparent tool to reveal the spin-resolved bunching
behavior.
