Two dice are thrown. The events A, B, C are as follows:
A = Getting an odd number on the first die.
B = Getting a total of 7 on the two dice.
C = Getting a sum ≥ 8 on the two dice.
Describe events:
(i) A' (ii) not B (iii) A or B (iv) B and C (v) A but not C (vi) B but not C (vii) B or C
Two dice are tossed.
∴ The sample space is:
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
Event A: Getting an odd number on the first die.
A = (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)}
Event B: Getting a total of 7 on the two dice.
B = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
Event C: Getting a sum on the two dice.
C = {(2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6)}
(i) A' = S - A
= {(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
A' = Getting an even number on the first die.
(ii) not B = B' = S - B = {(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,6), (3,1), (3,2), (3,3), (3,5), (3,6), (4,1), (4,2), (4,4), (4,5), (4,6), (5,1), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6)}
(iii) {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,5), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,3), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1)}
(iv) B and C =
(v) A but not C =
={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (3,1), (3,2), (3,3), (3,4), (5,1), (5,2)}
(vi) B but not C = [from (iv)]
= B.
(vii) = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6)}