Permutations contained in transitive subgroups

In the first paper in this series we estimated the probability that a random permutation π ∈ S _n has a fixed set of a given size. In this paper, we elaborate on the same method to estimate the probability that p has m disjoint fixed sets of prescribed sizes k ₁,..,k _m, where k ₁+···+k _m = n. We deduce an estimate for the proportion of permutations contained in a transitive subgroup other than S _n or A _n. This theorem consists of two parts: an estimate for the proportion of permutations contained in an imprimitive transitive subgroup, and an estimate for the proportion of permutations contained in a primitive subgroup other than S _n or A _n.