Dependence of the thermally assisted spin torque switching probability on the sweep electric current was investigated theoretically. The analytical expressions of the switching times for b = 1 and b = 2 are derived based on the rate equation, where b is the exponent of the current term in the switching rate. The switching current is approximately proportional to the temperature T and the logarithm of the sweep rate v for both b = 1 and b = 2 in the experimentally performed ranges of T and v. Experiments in very low temperature range are required to determine the exponent b.