  We consider a random self-affine carpet $F$ based on an $n\times m$
subdivision of rectangles and a probability $0<p<1$. Starting by dividing
$[0,1]^2$ into an $n\times m$ grid of rectangles and selecting these
independently with probability $p$, we then divide the selected rectangles into
$n\times m$ subrectangles which are again selected with probability $p$; we
continue in this way to obtain a statistically self-affine set $F$. We are
particularly interested in topological properties of $F$. We show that the
critical value of $p$ above which there is a positive probability that $F$
connects the left and right edges of $[0,1]^2$ is the same as the critical
value for $F$ to connect the top and bottom edges of $[0,1]^2$. Once this is
established we derive various topological properties of $F$ analogous to those
known for self-similar carpets.
