Football teams `T_(1)and T_(2)` have to play two games are independent. The probabilities of `T_(1)` winning, drawing and lossing a game against `T_(2)` are `1/6,1/6and 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

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`