Paragraph: Football teams $T_{1}$ and $T_{2}$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_{1}$ winning, drawing and losing a game against $T_{2}$ are $\frac{1}{2}, \frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets $3$ points for a win, $1$ point for a draw and $0$ point for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_{1}$ and $T_{2}$, respectively, after two games.
Question: $P(X>Y)$ is

• A

  $\frac{1}{4}$
• Correct answer
  B

  $\frac{5}{12}$
• C

  $\frac{1}{2}$
• D

  $\frac{7}{12}$

Hence, the correct answer is option: 'B'.