Two socks are to be picked at random from a drawer containing only bla

From the question stem and statement (1) we adopt the following:

(*) ASSUMPTION: We are dealing with two sequential extractions without replacement.

\(? = P\left( {2\,\,white\,\,from\,\,\left( * \right)} \right)\)

\(\left( 1 \right)\,\,{\text{black}}\,\,:\,\,{\text{white}}\,\,\, = \,\,\,1:2\,\,\,\,\,\,\left\{ \begin{gathered}\\
\,Take\,\,\left( {b,w} \right) = \left( {1,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = \frac{2}{3} \cdot \frac{1}{2} = \frac{1}{3}\,\,\,\, \hfill \\\\
\,Take\,\,\left( {b,w} \right) = \left( {2,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = \frac{4}{6} \cdot \frac{3}{5} \ne \frac{1}{3} \hfill \\ \\
\end{gathered} \right.\)

\(\left. {\left( 2 \right)\,\,{\text{white}} = 24\,\,\,\,\left\{ \begin{gathered}\\
\,Take\,\,\left( {b,w} \right) = \left( {1,24} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, \cong \,\,\,1\,\,\,\, \hfill \\\\
\,Take\,\,\left( {b,w} \right) = \left( {{{10}^6},24} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? \cong 0 \hfill \\ \\
\end{gathered} \right.\,\,\,} \right\}\,\,\,\,\,{\text{extremal}}\,\,{\text{evaluations}}\,\)

\(\left( {1 + 2} \right)\,\,\,\,\left\{ \begin{gathered}\\
black = 12 \hfill \\\\
{\text{white}} = 24 \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = \,\,{\text{unique}}\,\,\,\,\,\,\,\,\,\left( {\frac{{24}}{{36}} \cdot \frac{{23}}{{35}}} \right)\)

The above follows the notations and rationale taught in the GMATH method.

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