Consider a 3 game tournament between two teams Assume that every game results in either a win or loss The team that wins two or more games wins the seriesGATE CSE 2015

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Consider a 3 game tournament between two teams. Assume that every game results in either a win or loss. The team that wins two or more games wins the series.GATE CSE 2015

The probability for wining the first game for both teams is 1/2. The probability for a team to win a game after a win is 2/3. The probability of wining a game after a loss is 1/3. Note that the effect of only previous game is considered. What is the probability for a team to win the series after loosing first game.
A=1/9
B=1/6
C=2/9
D=1/3


By:milan-ransingh

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Answer: (C) A team has 3 chances(games) to win tournament. To win the tournament, a team must win atleast 2 games. Acc to question, Team looses first chances. Now, to win, it is must to win left 2 games. Probability to win the 2nd game : 1/3 (as previous game was a loss) Probability to win the 3rd game : 2/3 (as previous game was a win) So, Probability to win the tournament = 1/3 * 2/3 = 2/9
prajwalamv

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