A bag contains 1 ball with the number 1, 2 balls with the number 2, and 5 balls with the number 3. One ball is randomly drawn from the bag, the number on the ball is confirmed, and then it is returned. This trial is repeated 2 times. Let $\bar { X }$ be the average of the numbers on the drawn balls. What is the value of $\mathrm { P } ( \bar { X } = 2 )$? [4 points] (1) $\frac { 5 } { 32 }$ (2) $\frac { 11 } { 64 }$ (3) $\frac { 3 } { 16 }$ (4) $\frac { 13 } { 64 }$ (5) $\frac { 7 } { 32 }$
A bag contains 1 ball with the number 1, 2 balls with the number 2, and 5 balls with the number 3. One ball is randomly drawn from the bag, the number on the ball is confirmed, and then it is returned. This trial is repeated 2 times. Let $\bar { X }$ be the average of the numbers on the drawn balls. What is the value of $\mathrm { P } ( \bar { X } = 2 )$? [4 points]\\
(1) $\frac { 5 } { 32 }$\\
(2) $\frac { 11 } { 64 }$\\
(3) $\frac { 3 } { 16 }$\\
(4) $\frac { 13 } { 64 }$\\
(5) $\frac { 7 } { 32 }$