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

Options

A. `11/36`
B. `1/3`
C. `13/36`
D. `1/2`

Answer

C

Explanation

`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`