Question Number 7122 by 314159 last updated on 11/Aug/16
Answered by uchechukwu okorie favour last updated on 11/Aug/16
$${let}\:{the}\:{probability}\:{that}\:{a}\:{student} \\ $$$${picked}\:{at}\:{random}\:{be}\:{taller}\:{than} \\ $$$$\mathrm{1}.\mathrm{8}\:{metres}\:{be}\:{Pr}\left({T}\right) \\ $$$${Also};\:{let}\:{the}\:{probability}\:{that}\:{a} \\ $$$${student}\:{picked}\:{at}\:{random}\:{wear}\:{a} \\ $$$${spectacle}\:{be}\:{Pr}\left({S}\right) \\ $$$${Then}\:{the}\:{probability}\:{that}\:{the}\: \\ $$$${student}\:{is}\:{not}\:{taller}\:{than}\:\mathrm{1}.\mathrm{8}\:{metres} \\ $$$${is}\:{Pr}\left({T}'\right) \\ $$$${Also}\:{the}\:{probability}\:{that}\:{the}\: \\ $$$${student}\:{is}\:{not}\:{wearing}\:{spectacle} \\ $$$${is}\:{Pr}\left({S}^{'} \right) \\ $$$${Pr}\left({T}\right)=\mathrm{0}.\mathrm{2}=\frac{\mathrm{2}}{\mathrm{10}} \\ $$$${Pr}\left({T}^{'} \right)=\mathrm{1}−\mathrm{0}.\mathrm{2}=\mathrm{0}.\mathrm{8}=\frac{\mathrm{8}}{\mathrm{10}} \\ $$$${Pr}\left({S}\right)=\mathrm{0}.\mathrm{3}=\frac{\mathrm{3}}{\mathrm{10}} \\ $$$${Pr}\left({S}^{'} \right)=\mathrm{1}−\mathrm{0}.\mathrm{3}=\mathrm{0}.\mathrm{7}=\frac{\mathrm{7}}{\mathrm{10}} \\ $$$${let}\:{probability}\:{of}\:{the}\:{event}\: \\ $$$${happening}\:{be}\:{Pr}\left({E}\right) \\ $$$${Pr}\left({E}\right)={Pr}\left({TTT}^{'} \right)\cup{Pr}\left({SS}^{'} {S}^{'} \right) \\ $$$${Pr}\left({E}\right)=\left(\frac{\mathrm{2}}{\mathrm{10}}×\frac{\mathrm{2}}{\mathrm{10}}×\frac{\mathrm{8}}{\mathrm{10}}\right)\cup{Pr}\left(\frac{\mathrm{3}}{\mathrm{10}}×\frac{\mathrm{7}}{\mathrm{10}}×\frac{\mathrm{7}}{\mathrm{10}}\right) \\ $$$${Pr}\left({E}\right)=\frac{\mathrm{32}}{\mathrm{1000}}+\frac{\mathrm{147}}{\mathrm{1000}} \\ $$$${Pr}\left({E}\right)=\frac{\mathrm{179}}{\mathrm{1000}} \\ $$