Maths: probability question?

sample space of " 2 dices thrown , sum > 9 " ,
S = { (6,4) , (6,5) , (6,6) , (5,5) , (5,6) , (4,6) }

In sample space S , events of which " at least one dice = 6 "
= { (6,4) , (6,5) ,(6,6) , (4,6) , (5,6) }

∴ required probability = 5/6

[ Answer : D ]
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Note :-
This is a " CONDITIONAL probability " problem .
That means , you have to take what is "GIVEN" as the "sample space".
Here, it is : " sum > 9."

It is INCORRECT to take the sample space be all the events of throwing 2 dices !

Two fair dice are thrown. Given that the sum is greater than 9. What's the probability that at least one dice is a "6"?
A) 3/5
B) 2/3
C) 7/10
D) 5/6
Sol
A
　　　１　　２　　３　　４　　５　　６
１　　２　　３　　４　　５　　６　　７
２　　３　　４　　５　　６　　７　　８
３　　４　　５　　６　　７　　８　　９
４　　５　　６　　７　　８　　９　１０
５　　６　　７　　８　　９　１０　１１
６　　７　　８　　９　１０　１１　１２
B
　　　１　　２　　３　　４　　５　　６
　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ
２　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ
３　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ
４　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　１０
５　　Ｘ　　Ｘ　　Ｘ　　Ｘ　１０　１１
６　　Ｘ　　Ｘ　　Ｘ　１０　１１　１２
Ｃ
　　　１　　２　　３　　４　　５　　６
　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ
２　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ
３　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ
４　　Ｘ　　Ｘ　　Ｘ　　Ｘ　　Ｘ　１０
５　　Ｘ　　Ｘ　　Ｘ　　Ｘ　１０　１１
６　　Ｘ　　Ｘ　　Ｘ　１０　１１　１２
Answer=5/6
(D)





So I'd like to use '1 - P(both dices contain no "6")' to find the answer. The only possible outcome is (5，5)