Answer
(a) 0.9
(b) 0
(c) 0
(d) 0
(e) 0.1
Work Step by Step
Since they are mutually exclusive events:
A ∩ B = A ∩ C = B ∩ C = Ø and P(A ∩ B) = P(A ∩ C) = P(B ∩ C) = 0
(a) P(A U B U C) = P(A) + P(B) + P(C) = 0.2 + 0.3 + 0.4 = 0.9
(b) P(A ∩ B ∩ C) = P[(A ∩ B) ∩ C] = P(Ø ∩ C) = 0
(c) P(A ∩ B) = 0
(d) P[(A U B) ∩ C] = P[(A ∩ C) U (B ∩ C)] = 0
(e) P(A' ∩ B' ∩ C') = 1 - P(A) - P(B) - P(C) = 1 - 0.2 - 0.3 - 0.4 = 0.1
