1)

 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 points 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

   P(X>Y) is


A) $\frac{1}{4}$

B) $\frac{5}{12}$

C) $\frac{1}{2}$

D) $\frac{7}{12}$

Answer:

Option B

Explanation:

Here, P(X>Y) = P($T_{1}$ win) P($T_{1}$  win) +P( $T_{1}$  win )P ( draw) +P (draw) P ($T_{1}$  win)

                  =   $(\frac{1}{2}\times\frac{1}{2})+(\frac{1}{2}\times\frac{1}{6})+(\frac{1}{6}\times\frac{1}{2})=\frac{5}{12}$