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Question:
(3) 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 total of greater than or equal to 8 on the two dice. Describe the following events (a) AUB (b) A’ (c) B – C (d) B C
Answer:

When two dice are thrown, then total outcome = 6*6 = 36

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)}

Total outcome = 18

B: Getting a total of 7 on the two dice.

B = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Total outcome = 6

C: Getting a total of greater than or equal to 8 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)}

Total outcome = 15

1. n(A U B) = n(A) + n(B) - n(A ∩ B)

=> n(A U B) = 18 + 6 - 3

=> n(A U B) = 21

2. A complement = 36 - n(A) = 36 - 18 = 18

3. B - C = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)} = 6

4. B ∩ C = {(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)} = 21

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