We investigate the effectiveness of the hopping parameter expansion (HPE) combined with the Z(2) noise method in the calculation of the trace of the inverse of Wilsons Dirac operator and some other disconnected contributions.A numerical comparison of the standard deviation for the Z(2) noise method and HPE with the Z(2) noise method is carried out.It is found that there are noise reductions in all the quantities we calculated using the HPE with the Z(2) noise method.For the trace of the inverse of Wilsons Dirac operator,the HPE can reduce the statistical error by about 60％.