An agricultural research establishment grows vegetables and grades each one as either good or bad for its taste, good or bad for its size, and good or bad for its appearance. Overall 78% of the vegetables have a good taste. However, only 69% of the vegetables have both a good taste and a good size. Also, 5% of the vegetables have both a good taste and a good appearance, but a bad size. Finally, 84% of the vegetables have either a good size or a good appearance.
(a) If a vegetable has a good taste, what is the probability that it also has a good size?
(b) If a vegetable has a bad size and a bad appearance, what is the probability that it has a good taste?