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Read the passage and answer the questions.
In a Kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the…
In a Kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are $\frac{1}{2}, \frac{3}{10}$, and $\frac{1}{5}$ respectively.
Each team gets 5 points for win, 3 points for draw and 0 point for loss in a game. After two games, find the probability that:
(a)[2.0]
Jaipur has more points than Delhi.
(b)[2.0]
Jaipur and Delhi have equal points.
Answer
Answer (a)
Official answer keyP(Winning of Delhi) = P(Losing of Jaipur) $= \frac{1}{5}$; P(Losing of Delhi) = P(Winning of Jaipur) $= \frac{1}{2}$; P(Drawing of Delhi) = P(drawing of Jaipur) $= \frac{3}{10}$
Let X be the points of Jaipur after two games and Y be the points of Delhi after two games.
P(X > Y) = P(1st match win by Jaipur) P(2nd match win by Jaipur) + P(1st match win by Jaipur) P(2nd match draw by Jaipur) + P(1st match draw by Jaipur) P(2nd match win by Jaipur) $= \frac{1}{2}\cdot\frac{1}{2} + \frac{1}{2}\cdot\frac{3}{10} + \frac{3}{10}\cdot\frac{1}{2} = \frac{11}{20}$
| X | 10 | 8 | 6 | 3 | 0 |
| Y | 0 | 3 | 6 | 8 | 10 |
Answer (b)
Official answer keyP(X = Y) = P(1st match win by Jaipur) P(2nd match win by Delhi) + P(1st match win by Delhi) P(2nd match win by Jaipur) + P(1st match draw by Jaipur) P(2nd match draw by Delhi) $= \frac{1}{2}\cdot\frac{1}{5} + \frac{1}{5}\cdot\frac{1}{2} + \frac{3}{10}\cdot\frac{3}{10} = \frac{29}{100}$
From ISC 2025 Practice Mathematics, question 122.