A chess game between two grandmasters X and Y is won by whoever first wins a total of two games. X's chances of winning or loosing any perticular game are a, b and c, respectively. The games are independent and a+b+c=1.
The probability that Y wins the match after the 4th game, is

A chess game between Kamsky and Anand is won by whoever first wins 2 out of 3 games. Kamsky's chance of winning, drawing or lossing a particular game are p,q,r . The games are independent and p+q +r=1 . Prove that the probability that Kamsky wins the match is (p^2(P+3r))/((p+r)^3) .

In a given race, the odds in favour of horses A, B, C, D are 1:3, 1:4, 1:5 and 1:6 respectively. Find the probability that one of the them wins the race.

A, B and C in tum throw a die and one who gets a 6 first wins the game. A takes the first chance followed by B and C, and the process is repeated till one of them who gets a 6, wins the game. Find the probabilities of each for winning the game .

A and B throw two dice simultaneously turn by turn. A will win if he throws a total of 5, B will win if he throws a doublet. Find the probability that B will win the game, though A started the game .

In a T-20 tournament, there are five teams. Each teams plays one match against every other team. Each team has 50% chance of winning any game it plays. No match ends in a tie. Statement-1: The Probability that there is an undefeated team in the tournament is (5)/(16) . Statment-2: The probability that there is a winless team is the tournament is (3)/(16) .

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : 1/x+1/y=2/b .

A certain team wins with probability 0.7, loses with probability 0.2 and ties with probability 0.1. The team plays three games. Find the probability that the team wins at least two of the games, but not lose.

A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins if he gets a total of 10. If A starts the game, find the probability that B wins.