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 `1/2,1/6and 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(XgtY)` is

Options

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

Answer

B

Explanation

`P(XgtY)=T_(1)T_(1)+DT_(1)+T_(1)D("where"T_(1)" represents wins and D represents draw")`
`=((1)/(2)xx(1)/(2))+((1)/(6)xx(1)/(2))+((1)/(2)xx(1)/(6))=5/12`