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 losing or draw any particular 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 X wins the match after (n+1)th game (nge1) , 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

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 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

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 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

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) .

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

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

A bag contains a white and b black balls. Two players, A and B 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

Express each of the following linear equations in two variables in the standard form ax + by + c = 0 and in each case state the values of a, b and c : -3x+4y=12

An electric charge 10^6muC is placed at the origin (0, 0) of X-Y co-ordinate system. Two points A and B are situated at (sqrt2, sqrt2) and (2, 0) respectively. The potential difference between the points A and B will be