Of three events, A, B, and C, suppose events A and B are independent and events B

Question:

Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually exclusive. Their probabilities are P(A) = .7, P(B) = .2, and P(C) = .3. Express the following events in set notation and calculate their probabilities.
(a) Both B and C occur.
(b) At least one of A and B occurs.
(c) B does not occur.
(d) All three events occur.