a)
The exhaustative cases of two times throwing of a die is (Sample Space)
S = { (1,1),(1,2), (1,3), (1,4),
(2,1), (2,2), (2,3), (2,4),
(3,1), (3,2), (3,3), (3,4),
(4,1), (4,2), (4,3), (4,4), }
n = 16
b) i) A = { (1,1),(1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) }
ii) B = {(1,4), (2,4), (3,4), (4,1), (4,2), (4,3)}
iii) C = { (1,2), (1,4), (2,1), (2,3), (3,2), (3,4), (4,1), (4,3) }
iv) D = { (1,2), (1,3), (1,4), (2,3), (2,4), (3,4) }
c) i) True
ii) False
iii) False
iv) False
d) P(AUB) = P(A) + P(B) = 9/16 + 6/16 = 14/16
e) P(BUC) = P(B) + P(C) - P(B and C) = 6/16 + 8/16 - 3/16 = 11/16
f) P(CUD) = P(C) + P(D) - P(C and D) = 8/16 + 6/16 - 4/16 = 10/16
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