Question

Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players, the better-ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively, is

• A. $\frac{16}{31}$
• B. $\frac{1}{2}$
• C. $\frac{17}{31}$
• D. $\frac{11}{32}$

Answer 1

The correct option is A $\frac{16}{31}$

For ranked 1 and 2 players to be winners and runners up respectively, they should not be paired with each other in any round, except the last round. Therefore, the required probability = $\frac{30}{31}\times \frac{14}{15}\times \frac{6}{7}\times \frac{2}{3}=\frac{16}{31}$