Question

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 A wins all 4.

Answer 1

The probability that A wins a single game in the tournament is $\dfrac{6}{13}$. Since the outcomes of the games are independent, the probability that A wins all 4 games is $\left(\dfrac{6}{13}\right)^4 = \boxed{\dfrac{1296}{28561}}$.