Suppose P(ABC) = 0.05, P(AB) = 0.15, P(AC) = 0.2, P(BC) = 0.25, P(A) = P(B) = P(C) = 0.5. For each of the events given next, write the event using set notation in terms of A, B, and C, and compute the corresponding probability.
(a) At least one of the three events A,B,C occur.
(b) At most one of the three events occurs.
(c) All of the three events occurs.
(d) None of the three events occurs.
(e) At least two of the three events occurs.
(f) At most two of the three events occurs.