Two persons throw a dice alternately till one of them gets a 'six' and wins the game. Find their respective probabilities of winning.

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 and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning if A starts first.

A and B toss a coin alternately till one of them tosses a head and wins the game. If A starts the game, find their respective probability of winning.

A, B and C in tum throw a die and one who gets a 6 first wins the game. A takes the first chance followed by B and C, and the process is repeated till one of them who gets a 6, wins the game. Find the probabilities of each for winning the game .

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 hockey match two teams A and B scored same number of goals upto the end of the games so as to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.