Question Number 180735 by srikanth2684 last updated on 16/Nov/22
$${A}\:{and}\:{B}\:{throw}\:{with}\:\mathrm{3}\:{dice}.\:{if}\:{A}\: \\ $$$${throws}\:{a}\:{sum}\:{of}\:\mathrm{16}\:{points},\:{the} \\ $$$$\:{probability}\:{of}\:{B}\:{throwing}\: \\ $$$${a}\:{higher}\:{sum}\:{is}\: \\ $$$${pls}\:{solve} \\ $$
Answered by Acem last updated on 16/Nov/22
$${P}\left({B},\:>{sum}\right)=\:\frac{\mathrm{4}}{\mathrm{216}_{\mathrm{6}^{\mathrm{3}} } }=\:\frac{\mathrm{1}}{\mathrm{54}}\: \\ $$$$\:;\:\left(\mathrm{6},\:\mathrm{6},\:\mathrm{6}\right)\:,\:\left(\mathrm{6},\:\mathrm{6},\:\mathrm{5}\right)_{{has}\:\mathrm{3}\:{cases}} \\ $$
Commented by Acem last updated on 16/Nov/22
$${You}'{re}\:{welcome}! \\ $$$$ \\ $$$${B}'{s}\:{dice}\:{roll}\:{is}\:{independent}\:{of}\:{A}'{s}\:{one},\:{so}\:{it}'{s}\:{not} \\ $$$$\:{a}\:{conditional}\:{probability},\:{if}\:{you}\:{got}\:\left(\mathrm{6},\mathrm{6},\mathrm{1}\right)\:{it}'{s} \\ $$$$\:{likely}\:{that}\:{i}\:{get}\:{the}\:{same}\:{result}.\:{Your}\:{throw} \\ $$$$\:{doesn}'{t}\:{affect}\:{mine}. \\ $$$$ \\ $$$${Sample}\:{space}\: \\ $$$$\bullet\:{for}\:{one}\:{dice}\:{has}\:\mathrm{6}\:{results} \\ $$$$\bullet\:{for}\:{two}\:{dices}\:\mathrm{6}×\mathrm{6}\:{res}. \\ $$$$\:\left\{\left(\mathrm{1},\:\mathrm{1}\right),\:\left(\mathrm{1},\mathrm{2}\right)…\left(\mathrm{1},\:\mathrm{6}\right)\right. \\ $$$$\:\:\:\left(\mathrm{2},\:\mathrm{1}\right),\:………..\left(\mathrm{2},\:\mathrm{6}\right) \\ $$$$\:\:\:. \\ $$$$\:\:\:. \\ $$$$\:\left(\mathrm{6},\:\mathrm{1}\right)…………\left(\mathrm{6},\:\mathrm{6}\right) \\ $$$$\bullet\:{for}\:\mathrm{3}\:{dices}:\:\mathrm{6}×\mathrm{6}×\mathrm{6}\:{res}. \\ $$$$ \\ $$
Commented by srikanth2684 last updated on 16/Nov/22
$${thank}\:{you}\: \\ $$$${i}\:{have}\:{a}\:{doubt}\:{that}\:{what}\:{is}\:{sample} \\ $$$${space}?\:{is}\:{it}\:{a}\:{conditonal}\:{probability}? \\ $$
Commented by srikanth2684 last updated on 17/Nov/22
$${thank}\:{you} \\ $$