We investigate the full counting statistics (FCS) of spin-conserving and spin-flip charge transitions in Pauli-spin blockade regime of a GaAs double quantum dot. Experimentally, we executed real-time observation of charge transitions and constructed the FCS. A theoretical model is proposed to evaluate all spin-conserving and spin-flip tunnel rates. We enumerate advantages in FCS comparing to waiting time distribution for the evaluation with demonstration of the universal relation between FCS and waiting time distribution We report peculiar statistical features in the FCS, which appear in the system holding spin degeneracy and coexistence of slow and fast transitions. Our experimental results supported by the numerical calculation provide how the spin correlation plays on the full counting statistics. This study is potentially useful for elucidating the spin-related and other complex transition dynamics in classical and quantum systems.
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