20. a. By the formula for the probability of a general union,
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 0.3 + 0.6 − 0.2 = 0.7
b. Because (A ∪ B) ∩ C = ∅, then
P(C) = P(S) − P(A ∪ B) = 1 − .07.
c. By DeMorgan’s law for sets, Ac ∪ Bc = (A ∩ B)c = S − (A ∩ B). Hence, by the formula for
the probability of the complement of an event,
P(Ac ∪ Bc) = P(S − (A ∩ B)) = P(S) − P(A ∩ B) = 1 − 0.2 = 0.8.