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Question Number 131320 by mohammad17 last updated on 03/Feb/21

Answered by mr W last updated on 04/Feb/21

2: 1+1 ⇒(1/(36)) 3: 1+2, 2+1 ⇒(2/(36))=(1/(18)) 4: 2+2, 3+1, 1+3 ⇒(3/(36))=(1/(12)) 5: 2+3, 3+2, 1+4, 4+1 ⇒(4/(36))=(1/9) 6: 3+3, 2+4, 4+2, 1+5, 5+1 ⇒(5/(36)) 7: 3+4, 4+3, 2+5, 5+2,1+6,6+1 ⇒(6/(36))=(1/6) 8: 4+4, 3+5, 5+3, 2+6, 6+2 ⇒(5/(36)) 9: 4+5, 5+4, 3+6, 6+3 ⇒(4/(36))=(1/9) 10: 5+5, 4+6, 6+4 ⇒(3/(36))=(1/(12)) 11: 5+6, 6+5 ⇒(2/(36))=(1/(18)) 12: 6+6 ⇒(1/(36)) X p 2 1/36 3 1/18 4 1/12 5 1/9 6 5/36 7 1/6 8 5/36 9 1/9 10 1/12 11 1/18 12 1/36

$$\mathrm{2}:\:\mathrm{1}+\mathrm{1}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{36}} \\ $$$$\mathrm{3}:\:\mathrm{1}+\mathrm{2},\:\mathrm{2}+\mathrm{1}\:\Rightarrow\frac{\mathrm{2}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{18}} \\ $$$$\mathrm{4}:\:\mathrm{2}+\mathrm{2},\:\mathrm{3}+\mathrm{1},\:\mathrm{1}+\mathrm{3}\:\Rightarrow\frac{\mathrm{3}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\mathrm{5}:\:\mathrm{2}+\mathrm{3},\:\mathrm{3}+\mathrm{2},\:\mathrm{1}+\mathrm{4},\:\mathrm{4}+\mathrm{1}\:\Rightarrow\frac{\mathrm{4}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\mathrm{6}:\:\mathrm{3}+\mathrm{3},\:\mathrm{2}+\mathrm{4},\:\mathrm{4}+\mathrm{2},\:\mathrm{1}+\mathrm{5},\:\mathrm{5}+\mathrm{1}\:\Rightarrow\frac{\mathrm{5}}{\mathrm{36}} \\ $$$$\mathrm{7}:\:\mathrm{3}+\mathrm{4},\:\mathrm{4}+\mathrm{3},\:\mathrm{2}+\mathrm{5},\:\mathrm{5}+\mathrm{2},\mathrm{1}+\mathrm{6},\mathrm{6}+\mathrm{1}\:\Rightarrow\frac{\mathrm{6}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\mathrm{8}:\:\mathrm{4}+\mathrm{4},\:\mathrm{3}+\mathrm{5},\:\mathrm{5}+\mathrm{3},\:\mathrm{2}+\mathrm{6},\:\mathrm{6}+\mathrm{2}\:\Rightarrow\frac{\mathrm{5}}{\mathrm{36}} \\ $$$$\mathrm{9}:\:\mathrm{4}+\mathrm{5},\:\mathrm{5}+\mathrm{4},\:\mathrm{3}+\mathrm{6},\:\mathrm{6}+\mathrm{3}\:\Rightarrow\frac{\mathrm{4}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\mathrm{10}:\:\mathrm{5}+\mathrm{5},\:\mathrm{4}+\mathrm{6},\:\mathrm{6}+\mathrm{4}\:\Rightarrow\frac{\mathrm{3}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\mathrm{11}:\:\mathrm{5}+\mathrm{6},\:\mathrm{6}+\mathrm{5}\:\Rightarrow\frac{\mathrm{2}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{18}} \\ $$$$\mathrm{12}:\:\mathrm{6}+\mathrm{6}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{36}} \\ $$$$ \\ $$$${X}\:\:\:\:\:\:\:{p} \\ $$$$\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{1}/\mathrm{36} \\ $$$$\mathrm{3}\:\:\:\:\:\:\:\:\:\mathrm{1}/\mathrm{18} \\ $$$$\mathrm{4}\:\:\:\:\:\:\:\:\:\mathrm{1}/\mathrm{12} \\ $$$$\mathrm{5}\:\:\:\:\:\:\:\:\:\mathrm{1}/\mathrm{9} \\ $$$$\mathrm{6}\:\:\:\:\:\:\:\:\:\mathrm{5}/\mathrm{36} \\ $$$$\mathrm{7}\:\:\:\:\:\:\:\:\:\mathrm{1}/\mathrm{6} \\ $$$$\mathrm{8}\:\:\:\:\:\:\:\:\:\mathrm{5}/\mathrm{36} \\ $$$$\mathrm{9}\:\:\:\:\:\:\:\:\:\mathrm{1}/\mathrm{9} \\ $$$$\mathrm{10}\:\:\:\:\:\:\mathrm{1}/\mathrm{12} \\ $$$$\mathrm{11}\:\:\:\:\:\:\mathrm{1}/\mathrm{18} \\ $$$$\mathrm{12}\:\:\:\:\:\:\mathrm{1}/\mathrm{36} \\ $$

Commented by liberty last updated on 11/Feb/21

7: (1,6),(6,1),(2,5),(5,2),(3,4),(4,3)⇒(6/(36))=(1/6)

$$\mathrm{7}:\:\left(\mathrm{1},\mathrm{6}\right),\left(\mathrm{6},\mathrm{1}\right),\left(\mathrm{2},\mathrm{5}\right),\left(\mathrm{5},\mathrm{2}\right),\left(\mathrm{3},\mathrm{4}\right),\left(\mathrm{4},\mathrm{3}\right)\Rightarrow\frac{\mathrm{6}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{6}}\: \\ $$

Commented by mr W last updated on 04/Feb/21

yes, thanks!

$${yes},\:{thanks}! \\ $$

Answered by liberty last updated on 03/Feb/21

determinant ((Σ,2,3,4,5,6,7,8,9,(10),(11),(12)),((Freq),1,2,3,4,5,6,5,4,3,2,1),((prob),(1/(36)),(2/(36)),(3/(36)),(4/(36)),(5/(36)),(6/(36)),(5/(36)),(4/(36)),(3/(36)),(2/(36)),(1/(36))))

$$\begin{array}{|c|c|c|}{\Sigma}&\hline{\mathrm{2}}&\hline{\mathrm{3}}&\hline{\mathrm{4}}&\hline{\mathrm{5}}&\hline{\mathrm{6}}&\hline{\mathrm{7}}&\hline{\mathrm{8}}&\hline{\mathrm{9}}&\hline{\mathrm{10}}&\hline{\mathrm{11}}&\hline{\mathrm{12}}\\{\mathrm{Freq}}&\hline{\mathrm{1}}&\hline{\mathrm{2}}&\hline{\mathrm{3}}&\hline{\mathrm{4}}&\hline{\mathrm{5}}&\hline{\mathrm{6}}&\hline{\mathrm{5}}&\hline{\mathrm{4}}&\hline{\mathrm{3}}&\hline{\mathrm{2}}&\hline{\mathrm{1}}\\{\mathrm{prob}}&\hline{\frac{\mathrm{1}}{\mathrm{36}}}&\hline{\frac{\mathrm{2}}{\mathrm{36}}}&\hline{\frac{\mathrm{3}}{\mathrm{36}}}&\hline{\frac{\mathrm{4}}{\mathrm{36}}}&\hline{\frac{\mathrm{5}}{\mathrm{36}}}&\hline{\frac{\mathrm{6}}{\mathrm{36}}}&\hline{\frac{\mathrm{5}}{\mathrm{36}}}&\hline{\frac{\mathrm{4}}{\mathrm{36}}}&\hline{\frac{\mathrm{3}}{\mathrm{36}}}&\hline{\frac{\mathrm{2}}{\mathrm{36}}}&\hline{\frac{\mathrm{1}}{\mathrm{36}}}\\\hline\end{array} \\ $$$$ \\ $$

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