The Favard length of the planar $1/4$-corner Cantor set is $0$. Estimates exists about the rate with which the Favard length of the previous steps goes to $0$, but the exact rate of decay is unknown. However, if one considers a random construction of the $1/4$-corner Cantor set, things might seem better. In fact, Peres and Solomyak showed that the rate of decay for the average Favard length for the random $1/4$-corner Cantor set is of order exactly $1/n$. We show that the rate of decay for a random disk-like analogue has again order $1/n$. This suggests that any ``reasonable'' random Cantor set of positive and finite length might decay at the same rate.