We investigated the oxidative addition of PhX (X = Cl, Br) to a single Pd(0) atom or a PdX- complex in water using first-principles molecular dynamics simulations, with solvent H2O molecules explicitly included in the calculation models, to clarify the origin of the extremely high reactivity of a ligand-free Pd catalyst in an aqueous solution for the Suzuki-Miyaura reaction. The free-energy profiles are estimated using blue moon ensemble sampling to include the entropy effect in chemical reactions in a water solvent. The free-energy barrier of the oxidative addition step is quite low for PhBr, whereas the barrier for PhCl is sizable, indicating that the reaction can proceed at room temperature with a high rate for PhBr but a rather low rate for PhCl. We also investigated the effect of the additional halogen anion on the Pd catalyst as a "supporting ligand". The activation barrier of the oxidative addition step is not affected by the supporting halogen ligand, but the final state is significantly destabilized, which should be important for the following transmetalation step. The solvent effect has also been investigated and discussed.