On a given weekend in the fall a tire company can buy television and advertising time for a college football game a baseball game or a professional football game if the company sponsors the college football game there is a 80% chance of a high rating is 50% chance if they sponsor baseball game and a 70% chance if they sponsor professional football game the probabilities of the company sponsoring these various games are 0.5 0.3 and 0.2 respectively suppose the company does get a higher rating find the probability that it sponsored a professional football game