The aim of this article is to give a generalization of the concept of commutativity degree of a finite group G denoted by d(G) which is the probability that a randomly chosen pair (x, y) of elements of G commute, to the concept of relative commutativity degree of a subgroup H of a group G (denoted by d(H,G)). We shall state some results concerning the new concept which are mostly new or improvements of known results given by Lescot in 1995 and Moghaddam in 2005. Moreover, we shall define the relative n-th nilpotency degree of a subgroup of a group and give some results concerning this at the end
