All technicians are trained and rated $$qualified$$ or $$not qualified$$ by two managers: Lea and John. The ratings given by the two managers do not always match. Fifteen percent of technicians who are rated $$qualified$$ by Lea are rated $$not qualified$$ by John, and twenty percent of technicians who are rated $$not qualified$$ by Lea are rated $$qualified$$ by John. Historically, Lea gives a $$qualified$$ rating to eighty percent of the technicians. If a technician is rated $$qualified$$ by John, what is the probability that Lea would disagree?