QJEEAdv16Ma6098: JEE Advanced 2016 Mathematics - Class 12 JEEAdv16Ma6098 Solution: Football teams and have to play two games against each other.…

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QJEEAdv16Ma6098: JEE Advanced 2016 Mathematics - Class 12 JEEAdv16Ma6098 Solution: Football teams and have to play two games against each other.…

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 \over 2},{1 \over 6}

and

{1 \over 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.

$\,\,\,\,P\,\left( {X > Y} \right)$ is

Multiple Choice Options

A ${1 \over 4}$
B ${5 \over 12}$
C ${1 \over 2}$
D ${7 \over 12}$

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Accepted Answer

$\bullet$ 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)

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

QJEEAdv16Ma6098: JEE Advanced 2016 Mathematics - Class 12 JEEAdv16Ma6098 Solution: Football teams and have to play two games against each other.…

Multiple Choice Options

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