Question Number 43374 by peter frank last updated on 10/Sep/18
$$\mathrm{A}\:\mathrm{drawer}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{brown}\:\mathrm{socks}\:\mathrm{and}\:\mathrm{4} \\ $$$$\mathrm{blue}\:\mathrm{socks}\:\mathrm{well}\:\mathrm{mixed}.\:\mathrm{A}\:\mathrm{man}\:\mathrm{reaches} \\ $$$$\mathrm{the}\:\mathrm{drawer}\:\mathrm{and}\:\mathrm{pulls}\:\mathrm{out}\:\mathrm{2}\:\mathrm{socks}\:\mathrm{at} \\ $$$$\mathrm{random}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{they}\:\mathrm{match}? \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18
$${p}\left({brown}\right)=\frac{\mathrm{5}{c}_{\mathrm{2}} }{\mathrm{9}{c}_{\mathrm{2}} } \\ $$$${p}\left({blue}\right)\frac{\mathrm{4}{c}_{\mathrm{2}} }{\mathrm{9}{c}_{\mathrm{2}} } \\ $$$${rewuited}\:{snswer}=\frac{\mathrm{5}{c}_{\mathrm{2}} }{\mathrm{9}{c}}\:+\frac{\mathrm{4}{c}_{\mathrm{2}} }{\mathrm{9}{c}_{\mathrm{2}} }=\frac{\frac{\mathrm{5}×\mathrm{4}}{\mathrm{2}}+\frac{\mathrm{4}×\mathrm{3}}{\mathrm{2}}}{\frac{\mathrm{9}×\mathrm{8}}{\mathrm{2}}} \\ $$$$=\frac{\mathrm{16}}{\mathrm{36}}=\frac{\mathrm{4}}{\mathrm{9}} \\ $$$${pls}\:{che}\mathrm{4}{k}.. \\ $$$$ \\ $$