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# GATE | GATE-CS-2015 (Mock Test) | Question 17

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. 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

Explanation:

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 * 2/3Â

= 2/9

This solution is contributed by Mohit Gupta.

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