I think the instrument has the type of music lesson you are doing. If you are doing keyboard missions, then congratz.
As for the random prize, I have seen someone stacking instruments and increased their luck by a few thousand. It didn't really help them that much so i think the chance is fairly small.
Right, it doesn't work for all music lessons but only for those matching the instrument type.
For the random price: OK, I won't put much hope in it with my two cards :)
Thanks for your comment!