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. Assuming that the players are of equal strength. The probability that the player $S_1$ is among the eight winners is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{1}{4}$

Answer 1

Answer: (A)

$\frac{1}{2}$

Lets say that $S_1$ is paired with anyone from the remaining players
Since $S_1$ and his opponent have equal strength, therefore both of them will have equal chances of winning
Therefore, the probability of winning of $S_1=1/2$