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. `(1)/(4)`
B. `(5)/(12)`
C. `(1)/(2)`
D. `(7)/(12)`

Answer

B

Explanation

Here, `P(XgtY)=P(T_(1)"win")P(T_(1)"win")+P(T_(1)"win")P("draw")+P("draw")P(T_(1)"win")`
`=((1)/(2)xx(1)/(2))+((1)/(2)xx(1)/(6))+((1)/(6)xx(1)/(2))=(5)/(12)`