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 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
Attention reader! Don’t stop learning now. Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.
Learn all GATE CS concepts with Free Live Classes on our youtube channel.
This solution is contributed by Mohit Gupta.
Quiz of this Question