8n players $P_1,P_2,P_3\dots \dots ..P_{8n}$ play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 where the players are paired at random in each round. If it is given that $P_1$ wins in the third round. Find the probability that $P_2$ looses in the second round.

8n players $P_1,P_2,P_3,....,P_{8n}$ play a knock out tournament. It is known that all the players are of equal strngth. The tournat random is held in three rounds where the players are paired at random in each rouns. If it is given that $P_1$ wins in the third round. Find the probability than $P_2$ loses in the second round.

8 players $P_1,P_2,P_3,\dots ,P_8$ play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in three rounds where the players are paired at random in each round. If it is given that $P_1$ wins in the third round. If p be the probability that $P_2$ loses in second round, then the value of 7p is

Eight players $P_1,P_2,P_3,...........P_8$, play a knock out tournament. It is known that whenever the players $P_i\text{and}{P}_j$, play, the player $P_i$ will win if $i<j$. Assuming that the players are paired at random in each round, what is the probability that the players $P_4$, reaches the final ?

Players $P_1,P_2,P_3,P_4$ play knock out tournament. It is known that if $P_i,\text{and}{P}_j$, play, then $P_i$, will win if $i<j$ If they are paired at random for the first round, the probability that $P_3$ reaches the second round is

Sixteen players $P_1,P_2,P_3\dots ..,P_{16}$ play in tournament. If they grouped into eight pair then the probability that $P_4$ and $P_9$ are in different groups, is equal to

$P_1,P_2\dots ..,P_3$ an eight players participating in a tournament. If $I<j,$ then $P_i$ will win the match against $P_1$. Players are paired up randomly for first round and winners of this round again paired up for the second round and so on. The probability that $P_4$ reaches in the final, is

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.Find the probability that the player $S_1$ is among the eight winners.

Sixteen players $S_1,S_2,\dots ..S_{16}$ 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.
(i) Find the probability that the player $S_1$ is among the eight winners.
(ii) Find the probability that exactly one of the two players$S_1$ and $S_2$ is among the eight winners.

In a knockout tournament $2^n$ equally skilled players; $S_1.S_2.......S_{2^n}$are participating. In each roundplayers are divided in pair at random and winner from each pair moves in the next round. If $S_2$ reaches thesemifinal then the probability that $S_1$ wins the tournament is $\frac{1}{20}$. Find the value of $\text{'}n\text{'}$.

$2^n$ players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of two particular players $S_{1}and{S}_2,$ exactly one will reach in semi-final $(n\in N,n\ge 2)\stackrel{.}{}$