  This note provides a generalisation of a recent result by J\"arvenp\"a\"a,
J\"arvenp\"a\"a, Koivusalo, Li, and Suomala, (to appear), on the dimension of
limsup-sets of random coverings of tori. The result in this note is stronger in
the sense that it provides also a large intersection property of the
limsup-sets, the assumptions are weaker, and it implies the result of
J\"arvenp\"a\"a, J\"arvenp\"a\"a, Koivusalo, Li, and Suomala as a special case.
The proof is based on a recent result by Persson and Reeve from 2013.
