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 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

P(X=Y) is


A) $\frac{11}{36}$

B) $\frac{1}{3}$

C) $\frac{13}{36}$

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

Answer:

Option C

Explanation:

P[X=Y]=P(draw).P(draw)+ P( $T_{1}$ win )  P ( $T_{2}$ win)+ P(  $T_{2}$ win).P( $T_{1}$ win)

         $=(\frac{1}{6}\times \frac{1}{6})+ (\frac{1}{2}\times\frac{1}{3})+ (\frac{1}{3}\times\frac{1}{2})=\frac{13}{36}$