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**ovi8** A pair of dice is rolled. What are the odds in favor of each of the following events occuring?

a) a sum of 7 turning up

b) a sum of 11 turning up

c) a sum of 7 or a sum of 11 turning up

here is what i have so far..

a) n(S) = 6x6=36

E(rolling a 7) = {(1,6),(2,5),(4,3),(6,1),(5,2),(3,4)}

n(E)= 6

P(E)= 6/36 simplified 1/6

so getting the odds would be..

1/6 / 5/6 = 1/5

therefore the odds are 1 to 5

b) n(S) = 6x6=36

E(rolling a 11) = {(6,5),(5,6)}

n(E)= 2

P(E)= 2/36 simplified 1/18

so getting the odds would be..

1/18 / 17/18 = 1/17

therefore the odds are 1 to 17

c) a sum of 7 or a sum of 11 turning up

probability of rolling a 7 = 1/6

probability of rolling a 11 = 1/18

1/6x1/18 = 1/108

P(E)/P(E') = 1/108/107/108 = 1/107

therefore the odds are 1 to 107

any help would be greatly appreciated.