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 X wins the match, is

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 a out of 2 games. Kamsky's chance of winnig, drawing or lossing a particular game are 2. 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) .

A girl calculate the probability of her winning the game in a match and finds it 0.08. What is the probability of her losing 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) .

Football teams T_1 and T_2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_1 winning. Drawing and losing a game against T_2 are (1)/(2),(1)/(6) and (1)/(3) respectively. Each team gets 3 points for a win. 1 point for a draw and 10 pont for a loss in a game. Let X and Y denote the total points scored by teams T_1 and T_2 respectively. after two games.

Three groups A, B and C are contesting for positions on the Board of Directors of a company. The probability of their winning are 0.5, 0.3 and 0.2, respectively. If the froup A wins, then the probabilityof introducing a new product is 0.7 and the corresponding probabilies for groups B and C are 0.6 and 0.5, respectively. Find the probability that the new product will be introduced.

Football teams T_(1)and T_(2) have to play two games are independent. The probabilities of T_(1) winning, drawing and lossing a game against T_(2) are 1/2,1/6and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_(1) and T_(2) respectively, after two games. P(X=Y) is

A bag contains a white and b black balls. Two players, Aa n dB alternately draw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B , then find the ratio a : b

Two numbers b and c are chosen at random with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. The probability that x^2+bx+cgt0 for all x in R is