`5` players of equal strength play one each with each other. `P(A)=` probability that at least one player wins all matches he (they) play. `P(B)=` probability that at least one player losses all his (their) matches.

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.

If a probability of a player winning a particular tennis match is 0 . 72 . What is the probabillity of the player loosing the match ?

India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is

P_(1),P_(2),P_(3),.........,P_(8)are8 players of equal strength who play with each other in a knockout tournament.The probability that P_(1) wins against P_(2) and P_(3) to reach the final and also wins the tournament is p,then 42p is equal to

Team 'A' plays with 5 other teams exactly once. Assuming that for each match the probabilities of a win, draw and loss are equal then (consider that the outcomes of every match is either win or loss or draw) (A) The probability that A wins and losses equal number of matches is 34/81 (B) The probability that A wins and losses equal number of matches is 17/81

Consider 5 independent Bernoulli's trials , each with probability of success p . If the probability of at least one failure is greater p , If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval :

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