Solve the Problem $$\text { Find the optimal strategy for player } R \text {. }$$

Solve the problem.
-Player R has two cards: a red 2 and a black 8. Player C has three cards: a red 3, a black 5, and a black 10. They each show one of their cards. If the cards are the same color, C receives the larger of
The two numbers. If the cards are of different colors, R receives the sum of the two numbers. The
Payoff matrix is :
$$\text { Find the optimal strategy for player } R \text {. }$$

A)
$\hat{x}=\left[\begin{array}{l}\frac{19}{29} \\\frac{10}{29}\end{array}\right]$

B)
$\hat{x}=\left[\begin{array}{l}\frac{2}{3} \\\frac{1}{3}\end{array}\right]$

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

D)
$\hat{x}=\left[\begin{array}{l}\frac{10}{29} \\\frac{19}{29}\end{array}\right]$