Question Number 159159 by otchereabdullai@gmail.com last updated on 13/Nov/21
$$\:\mathrm{Three}\:\mathrm{students}\:\mathrm{are}\:\mathrm{runing}\:\mathrm{for}\:\mathrm{school} \\ $$$$\:\mathrm{SRC}\:\mathrm{president},\:\mathrm{kada}'\mathrm{s}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{winning}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{8}},\:\mathrm{Atiga}'\mathrm{s}\:\mathrm{probability}\: \\ $$$$\mathrm{of}\:\mathrm{winnig}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{kada}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{likely} \\ $$$$\mathrm{to}\:\mathrm{win}\:\mathrm{as}\:\mathrm{Apio}.\: \\ $$$$\mathrm{i}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{both}\: \\ $$$$\:\mathrm{Atiga}\:\mathrm{and}\:\mathrm{Apio}\:\mathrm{draw} \\ $$$$\mathrm{ii}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{only} \\ $$$$\mathrm{one}\:\mathrm{wins}\:\mathrm{the}\:\mathrm{presidency}. \\ $$
Answered by mr W last updated on 14/Nov/21
$${Kada}:\:{win}\:\frac{\mathrm{1}}{\mathrm{8}},\:{not}\:{win}\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$$${Atiga}:\:{win}\:\frac{\mathrm{1}}{\mathrm{3}},\:{not}\:{win}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${Apio}:\:{win}\:\frac{\mathrm{1}}{\mathrm{4}},\:{not}\:{win}\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left(\mathrm{1}\right) \\ $$$${both}\:{Atiga}\:{and}\:{Apio}\:{win}: \\ $$$${p}=\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\left(\mathrm{2}\right) \\ $$$${only}\:{one}\:{wins}\:{means}: \\ $$$${Atiga}\:{wins},\:{Apio}\:{not}\:{win},\:{Kada}\:{not}\:{win} \\ $$$${Apio}\:{wins},\:{Atiga}\:{not}\:{win},\:{Kada}\:{not}\:{win} \\ $$$${Kada}\:{wins},\:{Atiga}\:{not}\:{win},\:{Apio}\:{not}\:{win} \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}×\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{7}}{\mathrm{8}}×\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{7}}{\mathrm{8}}×\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{16}}+\frac{\mathrm{7}}{\mathrm{32}}+\frac{\mathrm{7}}{\mathrm{48}} \\ $$$$=\frac{\mathrm{41}}{\mathrm{96}} \\ $$$$\left(\mathrm{3}\right)\:\left({not}\:{asked},\:{but}\:{added}\:{by}\:{myself}\right) \\ $$$${all}\:{of}\:{them}\:{win} \\ $$$${p}=\frac{\mathrm{1}}{\mathrm{8}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{96}} \\ $$$$\left(\mathrm{4}\right)\:\left({not}\:{asked},\:{but}\:{added}\:{by}\:{myself}\right) \\ $$$${none}\:{of}\:{them}\:{wins},\:{i}.{e}.\:{all}\:{not}\:{win} \\ $$$${p}=\frac{\mathrm{7}}{\mathrm{8}}×\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{3}}{\mathrm{4}}=\frac{\mathrm{7}}{\mathrm{16}} \\ $$
Commented by mr W last updated on 14/Nov/21
$${please}\:{comfirm}\:{if}\:{you}\:{have}\:{the} \\ $$$${right}\:{answer}! \\ $$
Commented by otchereabdullai@gmail.com last updated on 14/Nov/21
$$\mathrm{please}\:\mathrm{no}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{question}\:\mathrm{but} \\ $$$$\mathrm{i}\:\mathrm{trust}\:\mathrm{your}\:\mathrm{anwer}\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}! \\ $$