An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: A: the sum is greater than 8, B: 2 occurs on either die C: the sum is at least 7 and a multiple of 3. Which pairs of these events

Answer

N/a

Explanation

When a pair of dice is thrown, the 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 a sum of two numbes moe than 8.
`=` event of getting the sum of two number as 9,10,11,12.
`={(3,6),(4,5),(5,4),(6,3),(4,6),(5,5)`,
`(6,4),(5,6),(6,5),(6,6)}`
`B=` event of getting 2 on atleast one die
`={(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)`
`(1,2),(3,2),(4,2),(5,2),(6,2)}`
`C=` event of getting the sum of numbers shown at least 7 and multile of 3
`{(3,6),(4,5),(5,4),(6,3)}`
Here `AnnB=phi,BnnC=phi` and `AnnC!=phi`
`:.` Events A and B are mutually exclusive.
Events B and C are nutually exclusive.