In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played?

Question

Felipe Burgess

Mathematics

30 March, 21:09

In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played?

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Answers (1)

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Graham Rich · Answer 1

1/8

Step-by-step explanation:

For the match to be finished after 3 games are played, it means that 1 person my win 3 games in a row.

Since each player has a 50% chance of winning, the chances of it would be

1/2*1/2*1/2 or (1/2) ^3

Therefore the answer is 1/8 chance