Khi tung 3 con xúc xắc, mỗi con có 6 mặt \(\Rightarrow\) tổng số kết quả có thể xảy ra là: \(6.6.6=216\left(cách\right)\)
Số trường hợp thua (tổng \(n=x+y+z< 10\))
\(n=3:\left(1,1,1\right)\Rightarrow1\left(cách\right)\)
\(n=4:\left(2,2,1\right),\left(1,2,1\right),\left(1,1,2\right)\Rightarrow3\left(cách\right)\)
\(n=5: (3,1,1),(1,3,1),(1,1,3),(2,2,1),(2,1,2),(1,2,2)\Rightarrow6\left(cách\right)\)
\(n=6:(4,1,1),(1,4,1),(1,1,4),(3,2,1),(3,1,2),(2,3,1),(2,1,3),(1,3,2),(1,2,3),(2,2,2)\Rightarrow10\left(cách\right)\)
\(n=7:\)
\((5,1,1),(1,5,1),(1,1,5),(4,2,1),(4,1,2),(2,4,1),(2,1,4),(1,4,2),(1,2,4),\text{(3,3,1),(3,1,3),(1,3,3),(3,2,2),(2,3,2),(2,2,3)}\)
\(\Rightarrow15\left(cách\right)\)
\(n=8:\)
\((6,1,1),(1,6,1),(1,1,6),(5,2,1),(5,1,2),(2,5,1),(2,1,5),(1,5,2),(1,2,5)\)
\((4,3,1),(4,1,3),(3,4,1),(3,1,4),(1,4,3),(1,3,4)\)
\((4,2,2),(2,4,2),(2,2,4),(3,3,2),(3,2,3),(2,3,3)\)
\(\Rightarrow21\left(cách\right)\)
\(n=9:\)
\((6,2,1),(6,1,2),(2,6,1),(2,1,6),(1,6,2),(1,2,6)\)
\((5,3,1),(5,1,3),(3,5,1),(3,1,5),(1,5,3),(1,3,5)\)
\((4,4,1),(4,1,4),(1,4,4),(5,2,2),(2,5,2),(2,2,5)\)
\((3,3,3),(4,3,2),(4,2,3),(3,4,2),(3,2,4),(2,4,3),(2,3,4)\)
\(\Rightarrow25\left(cách\right)\)
Tổng số trường hợp thua \(\left(n< 10\right)\)
\(1+3+6+10+15+21+25=81\left(cách\right)\)
\(\Rightarrow\) Số trường hợp thắng \(n\ge10:216-81=135\left(cách\right)\)
Xác suất để người chơi thắng là:
\(P\left(thắng\right)=\dfrac{135}{216}=0,625=62,5\%\)
