Question

Question #7ec9a

Answer 1

`9/11 (Answer D.)`

Explanation:

`P["sum" >= 8|"at least one dice shows 6"]`
`= "P[sum >= 8 AND at least one dice shows 6]" / "P[at least one dice shows 6]"`
`= (9/36) / (1 - (5/6)^2)`
`= (1/4) / (11/36)`
`= 9/11`
`(Answer D.)`

`P["sum>=8 AND at least one dice shows 6"] =`
`"9/36 because there are 9 good combinations out of the 36 :"`
`(6,2),(2,6),(6,3),(3,6),(6,4),(4,6),(6,5),(5,6), and (6,6).`

`P["at least one dice shows 6"] = 1 - P["no dice shows 6"]`
`= 1 - (5/6)^2`
`"Another possibility is using the formula for OR :"`
`"P[dice 1 is 6 OR dice 2 is 6]"`
`"= P[dice 1 is 6] + P[dice 2 is 6] - P[ dice 1 AND dice 2 is 6]"`
`= 1/6 + 1/6 - 1/(6*6)`
`= (6 + 6 - 1)/36`
`= 11/36`