$$\bullet$$ Probability of wining of T₁ against T₂ is = 1/2.

$$\bullet$$ Probability of drawing of T₁ against T₂ is = 1/6.

$$\bullet$$ Probability of losing of T₁ against T₂ is = 1/3.

$$\bullet$$3 points for win.

$$\bullet$$1 point for draw.

$$\bullet$$ 0 point for loss.

Here, P(X > Y) = P(T₁ win) P(T₁ win) + P(T₁ win) P(draw) + P(draw) P(T₁ win)

$$ = \left( {{1 \over 2} \times {1 \over 2}} \right) + \left( {{1 \over 2} \times {1 \over 6}} \right) + \left( {{1 \over 6} \times {1 \over 2}} \right) = {5 \over {12}}$$