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.)

Aa n dB participate in a tournament of best of 7 games. It is equally likely that either A wins or B wins or the game ends in a draw. What is the probability that A wins the tournament.

Some boys are playing a game, in which the stone thrown by them landing in a circular region (give in the figure ) is considered as win and landing other than the circular region is considered as loss. What is the probability to win the game ?

A and B throw a die alternatively till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts first.

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 persons A and B get together once a weak to play a game. They always play 4 games . From past experience Mr. A wins 2 of the 4 games just as often as he wins 3 of the 4 games. If Mr. A does not always wins or always loose, then the probability that Mr. A wins any one game is (Given the probability of A's wining a game is a non-zero constant less than one).

Two players P_1 , and P_2 , are playing the final of a chase championship, which consists of a series of match Probability of P_1 , winning a match is 2/3 and that of P_2 is 1/3. The winner will be the one who is ahead by 2 games as compared to the other player and wins at least 6 games. Now, if the player P_2 , wins the first four matches find the probability of P_1 , wining the championship.

A and B throw a die alternatively till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts first.

Aa n dB 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) a. 3//5 b. 2//5 c. 1//2 d. 4//5