  Answering questions of Itai Benjamini, we show that the event of complete
occupation in 2-neighbour bootstrap percolation on the d-dimensional box [n]^d,
for d\geq 2, at its critical initial density p_c(n), is noise sensitive, while
in k-neighbour bootstrap percolation on the d-regular random graph G_{n,d}, for
2\leq k\leq d-2, it is insensitive. Many open problems remain.
