  We discuss the nature of the two-stage percolation transition on the enhanced
binary tree in order to explain the disagreement in the estimation of the
second transition probability between the one in our recent paper (J. Phys.
A:Math. Theor. 42 (2009) 145001) and the one in the comment to it from Baek,
Minnhagen and Kim. We point out some reasons that the finite size scaling
analysis used by them is not proper for the enhanced tree due to its
nonamenable nature, which is verified by some numerical results.
