Question

Sixteen players $S_1,S_2,....S_{16}$ play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength.

The probability that the player $S_1$ is among the eight winners is $\frac{1}{k}$. Find the value of $k$.

Answer 1

Since all players are assumed to be of same strength,they will have same probability of winning.So when player $S_1$ plays his opponent,he will have probability of winning as $p=\frac{1}{2}$ (same as his opponent such that total probability$=\frac{1}{2}+\frac{1}{2}=1$)
Hence, $k=2$