Question

Sixteen players $S_1,S_2,\cdots ,S_{16}$ Play in a tournament.They are divided into eight play in a tounament. 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 on the basis of a game played between the two players of the pair. Assume that all the players are of equal Strength. Find the probability that the player $S_1$is among the eigth winners.

• A. $\frac{1}{16}$
• B. $\frac{1}{8}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

Answer: (A)

$\frac{1}{16}$

Here the probability of winning is $\frac{1}{2}\lambda$ for each player in a pair as all players are of equal strength.
So the player $S_1$will be among $8$ winners as there are $8$ pairs,
Hence the required probability $P\left(s_1\right)=\frac{1}{8}.\frac{1}{2}=\frac{1}{16}$