Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the number on the first dice le5. Describe the events (i) A' (ii) not B (iii) A or B (iv) A and B (v) A but not C (vi) B or C (vii) B and C (viii) AnnB'nnC'

Two dice are thrown. The events A, B and C are as follows: A: getting

1.	Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the number on the first dice le5. Describe the events (i) A' (ii) not B (iii) A or B (iv) A and B (v) A but not C (vi) B or C (vii) B and C (viii) AnnB'nnC'
Answer» SOLUTION :In a throw of two dice Sample space `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)):}}` Now `A=` event of getting an even number on first die `={{:((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)):}}` `B=` event of getting an odd number of first die `={{:((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)):}}` `C=` event of getting the sum NUMBERS less than or equal to 5 `={(1,1,),(1,2),(2,1),(1,3),(2,2),` `(3,1),(1,4),(2,3),(3,2),(4,1)}` `A'=S-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)):}}` (ii) not `B=S-B` `={{:((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)):}}` (iii) A or B `={{:((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)):}}` (iv) A and `B=phi` (v) A but not `C=A-C` `{(2,4),(2,5),(2,6),(4,2),(4,3),(4,4),(4,5),` `(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}` (vi) B or `C=BuuC` `={{:((1,1)","(1,2)","(1,3)","(1,4)","(1,5)","(1,6)),((2,1)","(2,2)","(2,3)),((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((4,1)), ((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)):}}` (VII) B and `C=BnnC` `={1,1),(1,2),(1,4),(3,1),(3,2)}` (viii) `C=S-C` `={{:((1,5)","(1,6)),((2,4)","(2,5)","(2,6)),((3,3)","(3,4)","(3,5)","(3,6)),((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)):}}` Now `AnnB'nnC'` `=AnnC' :' B'=A` (from PART II) `={{:((2,4)","(2,5)","(2,6)),((4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}`

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