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

Football teams `T_(1)and T_(2)` have to play two games are independent

1.	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(XgtY)` isA. `1/4`B. `5/12`C. `1/2`D. `7/12`
Answer» Correct Answer - B `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`

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