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Question Number 159159 by otchereabdullai@gmail.com last updated on 13/Nov/21

$$\mathrm{Three}\mathrm{students}\mathrm{are}\mathrm{runing}\mathrm{for}\mathrm{school}$$$$\mathrm{SRC}\mathrm{president},{\mathrm{kada}}^{\prime }\mathrm{s}\mathrm{probability}\mathrm{of}$$$$\mathrm{winning}\mathrm{is}\frac{1}{8},{\mathrm{Atiga}}^{\prime }\mathrm{s}\mathrm{probability}$$$$\mathrm{of}\mathrm{winnig}\frac{1}{3}\mathrm{and}\mathrm{kada}\mathrm{is}\mathrm{half}\mathrm{as}\mathrm{likely}$$$$\mathrm{to}\mathrm{win}\mathrm{as}\mathrm{Apio}.$$$$\mathrm{i}.\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{probability}\mathrm{that}\mathrm{both}$$$$\mathrm{Atiga}\mathrm{and}\mathrm{Apio}\mathrm{draw}$$$$\mathrm{ii}.\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{probability}\mathrm{that}\mathrm{only}$$$$\mathrm{one}\mathrm{wins}\mathrm{the}\mathrm{presidency}.$$

Answered by mr W last updated on 14/Nov/21

$$Kada:win\frac{1}{8},notwin\frac{7}{8}$$$$Atiga:win\frac{1}{3},notwin\frac{2}{3}$$$$Apio:win\frac{1}{4},notwin\frac{3}{4}$$$$\left(1\right)$$$$bothAtigaandApiowin:$$$$p=\frac{1}{3}\times \frac{1}{4}=\frac{1}{12}$$$$\left(2\right)$$$$onlyonewinsmeans:$$$$Atigawins,Apionotwin,Kadanotwin$$$$Apiowins,Atiganotwin,Kadanotwin$$$$Kadawins,Atiganotwin,Apionotwin$$$$=\frac{1}{8}\times \frac{2}{3}\times \frac{3}{4}+\frac{1}{3}\times \frac{7}{8}\times \frac{3}{4}+\frac{1}{4}\times \frac{7}{8}\times \frac{2}{3}$$$$=\frac{1}{16}+\frac{7}{32}+\frac{7}{48}$$$$=\frac{41}{96}$$$$\left(3\right)(notasked,butaddedbymyself)$$$$allofthemwin$$$$p=\frac{1}{8}\times \frac{1}{3}\times \frac{1}{4}=\frac{1}{96}$$$$\left(4\right)(notasked,butaddedbymyself)$$$$noneofthemwins,i.e.allnotwin$$$$p=\frac{7}{8}\times \frac{2}{3}\times \frac{3}{4}=\frac{7}{16}$$

Commented by mr W last updated on 14/Nov/21

$$pleasecomfirmifyouhavethe$$$$rightanswer!$$

Commented by otchereabdullai@gmail.com last updated on 14/Nov/21

$$\mathrm{please}\mathrm{no}\mathrm{answer}\mathrm{to}\mathrm{the}\mathrm{question}\mathrm{but}$$$$\mathrm{i}\mathrm{trust}\mathrm{your}\mathrm{anwer}\mathrm{God}\mathrm{bless}\mathrm{you}!$$

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