In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are 1 2 , 3 10 and 1 5 respectively. Each team gets 5 points for win, 3 points for draw and 0 points for loss in a game. After two games, find the probability that Jaipur has more points than Delhi.

Step-by-step solution

Let W, D, L denote the events of winning, drawing, and losing a game for Jaipur, with probabilities P(W) = 1 2 , P(D) = 3 10 , and P(L) = 1 5 . The points awarded are 5 for W , 3 for D , and 0 for L . Let S_J be the total points of Jaipur after two games. The possible outcomes for two games (G₁, G₂) and their corresponding points are: (W, W): 5+5=10 points, P = 1 2 1 2 = 1 4 (W, D): 5+3=8 points, P = 1 2 3 10 = 3 20 (D, W): 3+5=8 points, P = 3 10 1 2 = 3 20 (W, L): 5+0=5 points, P = 1 2 1 5 = 1 10 (L, W): 0+5=5 poi