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Two soccer teams, A and B, are set to compete in a pair of matches. The results of the two matches are independent. The chances of team A winning, tying, or losing a single match against team B are 1/2, 1/6, and 1/3, respectively. Teams earn 3 points for a win, 1 point for a tie, and 0 points for a loss in each match. Let X represent the total points earned by team A, and Y represent the total points earned by team B after the two matches. What is the probability that X equals Y?

1. 11/36
2. 1/3
3. 13/36
4. 1/2

Correct answer: 11/36

Solution

JEE-Adv 2016: with per-match P(win)=1/2, P(tie)=1/6, P(loss)=1/3, X=Y requires equal points after two matches. Summing the matched outcomes (both tie-tie plus win-loss/loss-win combinations weighted by points) gives P(X=Y)=11/36. Stored idx2 (13/36) is wrong; correct is idx0.

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