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 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 match between two players A and B is won by whoever first wins a total of two games. Probability of A's winning, drawng and losing any particular game are 1/6, 1/3 and 1/2 respectively. (The game are independent). If the probability that B wins the match in the 4^(th) gams is p , then 6p is equal to

A and B play a game of tennis. The situation of the game is as follows: if one scores two consecutive points after a deuce, he wins; if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is 2/3. The game is a deuce and A is serving. Probability that A will win the match is (serves are change after each game) 3//5 b. 2//5 c. 1//2 d. 4//5

Aa n dB play a series of games which cannot be drawn and p , q are their respective chance of winning a single game. What is the chance that A wins m games before B wins n games?

In a set of five games in between two players A and B, the probability of a player winning a game is 2/3 who has won the earlier game. A wins the first game, then the probability that A will win at least three of the next four games is (A) 4/9 (B) (64)/(81) (C) (32)/(81) (D) none of these

A tosses 2 fair coins & B tosses 3 fair cons after game is won by the person who throws greater number of heads. In case of a tie, the game is continued under identical rules until someone finally wins the game. The probability that A finally wins the game is K//11 , then K is

In an essay competition, the odds in favour of competitors P, Q, R S are 1:2, 1:3, 1:4, and 1:5 respectively. Find the probability that one then win the competitions.

Suppose the probability for A to win a game against B is 0.4. If A has an option of playing either a “best of 3 games'' or a “best of 5 games match against B, which option should be chosen so that the probability of his winning the match is higher? (No game ends in a draw.)

Suppose the probability for A to win a game against B is 0.4. If A has an option of playing either a “best of 3 games'' or a “best of 5 games match against B, which option should be chosen so that the probability of his winning the match is higher? (No game ends in a draw.)