Solve the Problem $\hat { y } = \left[ \begin{array} { c } 0 \\ \frac { 1 } { 2 } \\ \frac { 1 } { 2 } \end{array} \right]$

Solve the problem.
-Each player has a supply of nickels, dimes, and quarters. At a given signal, both players display one coin. If the displayed coins are not the same, then the player showing the higher valued coin
Gets to keep both. If they are both nickels or dimes, then player R keeps both; but if they are both
Quarters, then player C keeps both. Find the optimal strategy for player C.

A) $\hat { y } = \left[ \begin{array} { c } 0 \\ \frac { 1 } { 2 } \\ \frac { 1 } { 2 } \end{array} \right]$

B) $\hat { y } = \left[ \begin{array} { l } 0 \\ 1 \\ 0 \end{array} \right]$

C) $\hat { \mathrm { y } } = \left[ \begin{array} { c } 0 \\ \frac { 1 } { 3 } \\ \frac { 2 } { 3 } \end{array} \right]$

D) $\hat { \mathrm { y } } = \left[ \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right]$