This is prompted by my attempts to work on this question. Let $H \subset G \subseteq S_d$ be transitive permutation groups. Recall that an element of $S_d$ is called a derangement if it has no fixed points.

Is the proportion of derangements in $H$ always greater than in $G$?

If $H$ doesn't have to be transitive, then the answer is "no"; just let $H$ be trivial. But a quick sampling of examples with $G$ and $H$ both transitive doesn't turn up any counterexamples.

**UPDATE** Never mind. $A_4$ inside $S_4$, the probability of a derangement goes down from $3/8$ to $1/4$.

withoutan answer reappear just so. Those that reappear are thosewithanswer(s) that arestillin the 'unanswered' category, i.e. no accept answer and none with positive (or perhaps +2) score. (I once spend some time to check ca 2000 items in unanswered category looking for each question modified by the MO-user, ie having been bumped; very few havenoanswerandfor a couple of those thatcurrentlyhave none I checked, with kind help of Felipe Voloch, that theyused to haveone.) – quid Jul 24 '12 at 19:18