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`

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.

In the box there are a white and b black balls. Two persons A and B takes ball one after the other and each time ball is placed back in box. Person A starts the game. If white ball is obtained then person A wins the game probability of winning game by person A is double then the winning probability of person B. Then a : b = .........

A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, then find the probability of winning the game by A in third throw of the pair of dice.

A bag X contains 3 white and 2 black balls; another bag Y contains 2 white and 4 black balls. A bag and a ball out of it is picked at random. What is the probability that the ball is white?

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that One ball is red and two balls are white

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box, if atleast one black ball is to be included in the draw is ……

A box contains two white, there black and four red balls. In how many ways can there balls be drawn from the box, if atleast one black ball is to be included in the draw ?

An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.

A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.