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Question-210919




Question Number 210919 by RojaTaniya last updated on 22/Aug/24
Answered by mr W last updated on 22/Aug/24
yes, we can design such two dices.  the first one is a normal die  with six faces which have digit   1,2,3,4,5,6 respectively.  the second die is a special die.  three faces from it have digit 0  and the other three faces have   digit 6.  when you roll these two dices, the  probability that the sum of the  numbers appearing on their faces   is equallly likely to be any number  from 1 to 12, namely  p_(sum=1) =p_(sum=2) =...=p_(sum=12) =(3/(36))=(1/(12))
$${yes},\:{we}\:{can}\:{design}\:{such}\:{two}\:{dices}. \\ $$$${the}\:{first}\:{one}\:{is}\:{a}\:{normal}\:{die} \\ $$$${with}\:{six}\:{faces}\:{which}\:{have}\:{digit}\: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:{respectively}. \\ $$$${the}\:{second}\:{die}\:{is}\:{a}\:{special}\:{die}. \\ $$$${three}\:{faces}\:{from}\:{it}\:{have}\:{digit}\:\mathrm{0} \\ $$$${and}\:{the}\:{other}\:{three}\:{faces}\:{have}\: \\ $$$${digit}\:\mathrm{6}. \\ $$$${when}\:{you}\:{roll}\:{these}\:{two}\:{dices},\:{the} \\ $$$${probability}\:{that}\:{the}\:{sum}\:{of}\:{the} \\ $$$${numbers}\:{appearing}\:{on}\:{their}\:{faces}\: \\ $$$${is}\:{equallly}\:{likely}\:{to}\:{be}\:{any}\:{number} \\ $$$${from}\:\mathrm{1}\:{to}\:\mathrm{12},\:{namely} \\ $$$${p}_{{sum}=\mathrm{1}} ={p}_{{sum}=\mathrm{2}} =…={p}_{{sum}=\mathrm{12}} =\frac{\mathrm{3}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{12}} \\ $$
Commented by mr W last updated on 22/Aug/24
Commented by mr W last updated on 23/Aug/24
after some “try & error” i came  to this concept. i′m not sure if there  are other solutions.
$${after}\:{some}\:“{try}\:\&\:{error}''\:{i}\:{came} \\ $$$${to}\:{this}\:{concept}.\:{i}'{m}\:{not}\:{sure}\:{if}\:{there} \\ $$$${are}\:{other}\:{solutions}. \\ $$

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