In this paper, G is a metacyclic 2-group of positive type of nilpotency of class at least three. Let Ω be the set of all subsets of all commuting elements of G of size two in the form of (a, b) where a and b commute and each of order two. The probability that an element of a group fixes a set is considered as one of the extensions of the commutativity degree that can be obtained by some group actions on a set. In this paper, we compute the probability that an element of G fixes a set in which G acts on a set, Ω by conjugation.