Among 110 students in a probability class, on a three-problem exam, 30 get problem 1 incorrect, 40 get problem 2 incorrect, and 23 get problem 3 incorrect. Further, 20 students get both problems 1 and 2 incorrect, 15 get both problems 2 and 3 incorrect, and 8 get both problems 1 and 3 incorrect, and 7 get all three problems incorrect. Find the probability that a randomly selected student:
(a) Gets problem 1 incorrect but gets problem 2 correct.
(b) Gets problems 2 and 3 incorrect but gets problem 1 correct.
(c) Gets all three problems correct.