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

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

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is (A) 3/5 (B) 1/5 (C) 2/5 (D) 4/5

In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

The sum of two positive quantities is equal to 2ndot the probability that their product is not less than 3/4 times their greatest product is a. 3//4 b. 1//4 c. 1//2 d. none of these

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 players toss 4 coins each. The probability that they both obtain the same number of heads is a. 5//256 b. 1//16 c. 35//128 d. none of these

The probability of winning a race by three persons A ,B , and C are 1/2, 1/4 and 1/4 , respectively. They run two races. The probability of A winning the second race when B , wins the first race is (A) 1/3 (B) 1/2 (C) 1/4 (D) 2/3

2n boys are randomly divided into two subgroups containint n boys each. The probability that the two tallest boys are in different groups is a. n//(2n-1) b. (n-1)//(2n-1) c. (n-1)//4n^2 d. none of these

116 people participated in a knockout tennis tournament. The players are paired up in the first round, the winners of the first round are paired up in the second round, and so on till the final is played between two players. If after any round, there is odd number of players, one player is given a by, i.e. he skips that round and plays the next round with the winners. The total number of matches played in the tournment is

Forty team play a tournament. Each team plays every other team just once. Each game results in a win for one team. If each team has a 50% chance of winning each game, the probability that the end of the tournament, every team has won a different number of games is a. 1//780 b. 40 !//2^(780) c. 40 !//2^(780) d. none of these