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Football teams T(1) and T(2) have to pla...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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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