🚀 go-pugleaf

This is what a grade 11 maths C student cops for an assignment.
Solve this and your a LEGEND!

A lecturer has three favourite questions, one of which occurs in every exam
she sets.  The students know her habits in exam setting well.  She never
uses the same question twice in a row.  If she used question one last time,
she tosses a coin, and uses question two if a head comes up.  If she used
question two, she tosses two coins and switches to question three if both
come up heads.  If she used question three, she tosses three coins and
switches to question one if all three come up heads.  In the long run, find
which question she uses most often and how frequently it is used.