Each bag in a large box contains 25 tulip bulbs. Three-fourths of the bags are of Type A containing bulbs for 5 red and 20 yellow tulips; one-fourth of the bags are of Type B contain bulbs for 15 red and 10 yellow tulips. A bag is selected at random and one bulb is planted. What is the probability that the bulb will produce a red tulip? What is the probability that the bulb will produce a yellow tulip? If the tulip is red, what is the probability that a bag having 15 red and 10 yellow tulips was selected?