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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=Y)` is A. `(11)/(36)` B. `(1)/(3)` C. `(13)/(36)` D. `(1)/(2)` Select the correct answer from above options

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Correct Answer - C `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`

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