One bag contains 3 white and 2 black balls, another bag contains 5 white and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white?

Consider the following in respect to two events A and B

I. P(A occurs but not B) = P(A) $$-$$ P(B) if B $$ \subset $$ A

II. P(A alone or B alone occurs) = P(A) + P(B) $$-$$ P(A $$\cap$$ B)

III. P(A $$\cup$$ B) = P(A) + P(B) if A and B are mutually exclusive

Which of the above is/are correct?

A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?

A bag contains 20 books out of which 5 are defective. If 3 of the books are selected at random and removed from the bag in succession without replacement, then what is the probability that all three books are defective?