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

Thirty-two players ranked 1 to 32 are playing in 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 p, then the value of [2//p] is, where [.] represents the greatest integer function,_____.

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 (0,0) and the circumcenter is (1,2), 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 3//4 b. 1//4 c. 1//2 d. none of these

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 decided to the basis of a game played between the two players of the pair. Assume that all the players are of equal strength. (a) Find the prabability that the player S_(1) is among the eight winners. (b) Find the probability that exactly one of the two players S_(1)and S_(2) is among the eight winners.

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 eh two tallest boys are in different groups is n//(2n-1) b. (n-1)//(2n-1) c. (n-1)//4n^2 d. none of these