Out of the 50 colleges in a certain state, 25 are private, 15 offer engineering majors, and

Question:

Out of the 50 colleges in a certain state, 25 are private, 15 offer engineering majors, and 5 are
private colleges offering engineering majors. Find the probability that a college selected at random from the state
(a) offers an engineering major.
(b) offers an engineering major, given that it is public.
(c) is private, given that it offers an engineering major.
(d) is public, given that it offers an engineering major.