Solution
= Solution
In <site percolation> on the three-dimensional cubic lattice, each vertex $v\in\mathbb Z^3$ is independently open with probability $p$ and closed with probability $1-p$. Thus $\mathbb P_p$ is the Bernoulli product measure on $\{0,1\}^{\mathbb Z^3}$, and open paths are nearest-neighbour paths all of whose vertices are open.