A Bag Contains ‘m’ White And ‘n’ Black Balls. Two Players A And B Alternately Draw A Ball From The Bag, Replacing The Ball Each Time After Draw. A Beings The Game. If The Probability Of A Wining (that Is Drawing A White Ball) Is Twice The Probability Of B Wining, Then The Ratio m: n is Equal To:

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A bag contains ‘m’ white and ‘n’ black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after draw. A beings the game. If the probability of A wining (that is drawing a white ball) is twice the probability of B wining, then the ratio mn is equal to:


Correct option is

1: 1

Ai = A wins in ith try

Bi = B wins in ith try

⇒ P(A wins) = P(A wins in 1st attempt) + P(A wins in 2ndattempt)+…..∞                        




The above series is a G.P. with infinite terms, where common ratio 

⇒ P(B wins) = 1 – P(A wins)        (∵ There is no possible of draw)


It is given that P(A) = 2P(B)   



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