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Question

Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 12,16 and 13, 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 T1 and T2, respectively, after two games.

P(X>Y) is

A
14
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B
512
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C
12
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D
712
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Solution

The correct option is B 512
P(X>Y)=P(T1 wins both the matches)+P(T1 wins either of matches and other is draw )
P(X>Y)=(12×12)+(16×12+12×16)
P(X>Y)=512

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