In this paper, we are concerned with probabilistic high order numerical schemes
for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic PDEs,
it is shown by Cheridito, Soner, Touzi and Victoir  that the associated exact
solutions admit probabilistic interpretations, i.e., the solution of a fully
nonlinear parabolic PDE solves a corresponding second order forward backward
stochastic differential equation (2FBSDEs). Our numerical schemes rely on
solving those 2FBSDEs, by extending our previous results [W. Zhao, Y. Fu and T.
Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751.]. Moreover, in our
numerical schemes, one has the flexibility to choose the associated forward SDE,
and a suitable choice can significantly reduce the computational complexity.
Various numerical examples including the HJB equations are presented to show the
effectiveness and accuracy of the proposed numerical schemes.