a.
Không gian mẫu có 36 phần tử.
b. Ta có:
\({\Omega _A} = \left\{ \begin{array}{l}\left( {1;1} \right),\left( {1;2} \right),\left( {1;3} \right),\left( {1;4} \right),\left( {1;5} \right),\left( {1;6} \right)\\\left( {2;1} \right),\left( {2;2} \right),\left( {2;3} \right),\left( {2;4} \right),\left( {2;5} \right),\\\left( {3;1} \right),\left( {3;2} \right),\left( {3;3} \right),\left( {3;4} \right),\left( {4;1} \right),\\\left( {4;2} \right),\left( {4;3} \right),\left( {5;1} \right),\left( {5;2} \right),\left( {6;1} \right)\end{array} \right\}\)
Tập \({\Omega _A}\) có \(21\) phần tử.
Vậy \(\displaystyle P\left( A\right) = {{21} \over {36}}= {{7} \over {12}}\).
c. \({\Omega _B} = \left\{ \begin{array}{l}\left( {6;1} \right),\left( {6;2} \right),\left( {6;3} \right),\left( {6;4} \right),\\\left( {6;5} \right),\left( {6;6} \right),\left( {1;6} \right),\left( {2;6} \right),\\\left( {3;6} \right),\left( {4;6} \right),\left( {5;6} \right)\end{array} \right\}\)
Tập \({\Omega _B}\) có \(11\) phần tử.
Vậy \(\displaystyle P\left( B\right) = {{11} \over {36}}\).
\({\Omega _C} = \left\{ \begin{array}{l}\left( {6;1} \right),\left( {6;2} \right),\left( {6;3} \right),\left( {6;4} \right),\left( {6;5} \right),\\\left( {1;6} \right),\left( {2;6} \right),\left( {3;6} \right),\left( {4;6} \right),\left( {5;6} \right)\end{array} \right\}\)
Vậy \({\Omega _C}\) có \(10\) phần tử.
Do đó \(\displaystyle P\left( C \right) = {{10} \over {36}} = {5 \over {18}}.\)