QJEEAdv16Ma7841: JEE Advanced 2016 Mathematics - Class 12 JEEAdv16Ma7841 Solution: Football teams T 1 and T 2 have to play two games against each…

Question

Verified Solution • 2025–26 Session moderate

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

\frac{1}{2}, \frac{1}{6}

and

\frac{1}{3}

respectively. Each team gets

3

points for a win,

1

point for a draw and

0

point 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.

$P (X = Y)$ is

Accepted Answer

$∙$ Probability of wining of T₁ against T₂ = 1/2.

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

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

$∙$ 3 points for win.

$∙$ 1 point for draw.

$∙$ 0 point for loss.

P[X = Y] = P(draw) . P(draw) + P(T₁ win) P(T₂ win) + P(T₂ win) . P(T₁ win)

= (1/6 $\times$ 1/6) + (1/2 $\times$ 1/3) + (1/3 $\times$ 1/2) = 13/36

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