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Football teams `T_(1)` and `T_(2)` have to play two games against each other. It is assumed that the outcomes of the two games are independent. The pr

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Football teams `T_(1)` and `T_(2)` have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of `T_(1)` winning,drawing and losing a game against `T_(2)` are `(1)/(2),(1)/(6)` and `(1)/(3)`, respectively. Each teams gets 3 points for a win, 1 point of a drawn and 0 point for a loss in a games. `P(X gtT)` is A. `(1)/(4)` B. `(5)/(12)` C. `(1)/(2)` D. `(7)/(12)` Select the correct answer from above options

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Correct Answer - B 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)`

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