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Football teams T1 and T2 have to play tw...

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 team gets 3 points for a win. 1 point for a draw and 10 pont 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.

A

`11/36`

B

`1/3`

C

`13/36`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
`P(X=Y)=DD+T_(1)T_(2)+T_(2)T_(1)`
`=((1)/(6)xx(1)/(6))+((1)/(2)xx(1)/(3))+((1)/(3)xx(1)/(2))=13/36`
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