JEE Advanced 2016 Paper 2 Mathematics Q16

Mathematics

Problem

PARAGRAPH 1 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

\frac12

\frac16

and

\frac13

, 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)