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 `(1)/(2),(1)/(6) and (1)/(3)` respectively. Each team gets 3 points for a win. 1 point for a draw and 0 pont 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.

Options

A. `11/36`
B. `1/3`
C. `13/36`
D. `1/2`

Answer

C

Explanation

`P(X=Y)=DD+T_(1)T_(2)+T_(2)T_(1)`
`=((1)/(6)xx(1)/(6))+((1)/(2)xx(1)/(3))+((1)/(3)xx(1)/(2))=13/36`