`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_1a n dS_2,` exactly one will reach in semi-final `(n in N ,ngeq2)dot`

2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is

Thirty two players ranked 1 to 32 are playing is 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) 16/31 (B) 1/2 (C) 17/31 (D) none of these

Out of (2n +1) tickets cosecutively numbered, three are drawn of random, find the probability that the three number on them are in A.P.

If 3 tickets are drawn randomly from 2n tickets numbered 1, 2, 3,………,2n, find the probability that the numbers on the chosen tickets are in arithmetic progression.

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

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,.....10}dot Then find the probability that |x-y|> 5.

Find out the correct answer out of the options given against each questions : In a simple random sampling with replacement from a population of size N, the probability that a particular member is included in the selected sample of size n is

An urn contains N (=N_(1) + N_(2)) balls of which N_(1) are white and N_(2) red. If n balls are drawn at random, find the probability that among these exactly m balls are white.

A neutral atom has 2k, 8L, 8M and 2N electrons. Find out the total number of s-electron.

The equivalent resistance of series ad parallel combinations of two cells are S and P respectively. IF S=nP , then find out the minimum possible value of n.