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]=P("draw").P("draw")+P(T_(1)"win")P(T_(2)"win")+P(T_(2)"win").P(T_(1)"win")`
`=(1//6xx1//6)+(1//2xx1//3)+(1//3xx1//2)=13//36`