Team A and B play 13 games of chess of which 6 are won by A, 4 are won by B and 3 end in a draw. They agree to play a tournament of 4 games. Find the probability that B wins at least two games:

1 answer

In order to find the probability that B wins at least two games in the tournament, we need to consider the possible outcomes.

There are three possible outcomes for each game in the tournament: B wins, A wins, or it ends in a draw.

Since they agree to play 4 games, there are 3^4 = 81 possible outcomes.

We can use combinations to determine the number of outcomes where B wins at least two games.

If B wins all 4 games, there is only 1 possible outcome.

If B wins 3 games and A wins 1 game, there are 4 possible outcomes (B wins the first, second, third, or fourth game).

If B wins 2 games and A wins 2 games, there are (4 choose 2) = 6 possible outcomes.

Therefore, there are a total of 1 + 4 + 6 = 11 outcomes where B wins at least two games.

The probability that B wins at least two games is then 11/81, or approximately 0.136.