Probability - II

PARAGRAPH 1Football 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

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JEE Advanced 2016

PARAGRAPH 1Football 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

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JEE Advanced 2016

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JEE Advanced 2012