`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.

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).

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 ?

Three persons A,B,C take part in a competition.A is 4 times as likely as B to win,and B is thrice as likely as C to win .Find the probability of A,B,C to win the competition.

Forty team play a tournament. Each team plays every other team just once. Each game results in a win for one team. If each team has a 50% chance of winning each game, the probability that he end of the tournament, every team has won a different number of games is 1//780 b. 40 !//2^(780) c. 40 !//2^(780) d. none of these

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 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

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

In a game a coin is tossed 2n+m times and a player wins if he does not get any two consecutive outcomes same for at least 2n times in a row. The probability that player wins the game is a. (m+2)/(2^(2n)+1) b. (2n+2)/(2^(2n)) c. (2n+2)/(2^(2n+1)) d. (m+2)/(2^(2n))