In the senior year of a high school graduating class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but neither mathematics nor psychology, 10 studied all three subjects, and 8 did not take any of the three. Randomly selecta student from the class and find the probabilities of the following events.
(a) A person enrolled in psychology takes all three subjects.
(b) A person not taking psychology is taking both history and mathematics.