In explaining the physical origin of the jet composition of gamma-ray bursts ( GRBs ) , a more general picture , i.e . the hybrid jet model ( which introduced another magnetization parameter \sigma _ { 0 } on the basis of the traditional fireball model ) , has been well studied in Gao & Zhang . However , it still has not yet been applied to a large GRB sample . Here , we first employ the “ top-down ” approach of Gao & Zhang to diagnose the photosphere properties at the central engine to see how the hybrid model can account for the observed data as well , through applying a Fermi GRB sample ( eight bursts ) with the detected photosphere component , as presented in Li ( our Paper I ) . We infer all physical parameters of a hybrid problem with three typical values of the radius of the jet base ( r _ { 0 } = 10 ^ { 7 } , 10 ^ { 8 } , and 10 ^ { 9 } cm ) . We find that the dimensionless entropy for all the bursts shows \eta \gg 1 while the derived ( 1+ \sigma _ { 0 } ) for five bursts ( GRB 081224 , GRB 110721A , GRB 090719 , GRB 100707 , and GRB 100724 ) is larger than unity , indicating that in addition to a hot fireball component , another cold Poynting-flux component may also play an important role . Our analysis also shows that in a few time bins for all r _ { 0 } in GRB 081224 and GRB 110721A , the magnetization parameter at \sim 10 ^ { 15 } cm ( 1+ \sigma _ { r 15 } ) is greater than unity , which implies that internal-collision-induced magnetic reconnection and turbulence may be the mechanism to power the nonthermal emission , rather than internal shocks . We conclude that the majority of bursts ( probably all ) can be well explained by the hybrid jet problem .