Question

If you have a collection of 6 pairs of white socks and 3 pairs of black socks. What is the probability that a pair you pick without looking is
(i) white?
(ii) black?

Answer 1

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{pairs}\mathrm{of}\mathrm{white}\mathrm{socks}=6 \\ \mathrm{Number}\mathrm{of}\mathrm{pairs}\mathrm{of}\mathrm{black}\mathrm{socks}=3 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{pairs}\mathrm{of}\mathrm{socks}=6+3=9 \\ \therefore \mathrm{Number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}=9 \\ \left(\mathrm{i}\right) \\ \mathrm{Let}\mathrm{A}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{pair}\mathrm{of}\mathrm{white}\mathrm{socks}. \\ \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{6}{9}=\frac{2}{3} \\ \left(\mathrm{ii}\right) \\ \mathrm{Let}\mathrm{B}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{pair}\mathrm{of}\mathrm{black}\mathrm{socks}. \\ \therefore \mathrm{P}\left(\mathrm{B}\right)=\frac{3}{9}=\frac{1}{3} \end{gathered}$$