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 numbers on the dice 5.Describe the events

Answer

N/a

Explanation

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)):}}`