JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Probability XII

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)

Answer: (B)

Solution

P (X > Y)

occurs when

T_{1}

wins both games or wins one and draws the other.

P (both wins) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}

P (one win, one draw) = 2 \times \frac{1}{2} \times \frac{1}{6} = \frac{1}{6}

. Total:

\frac{1}{4} + \frac{1}{6} = \frac{5}{12}

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Single correct option