Question
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:

1: 2

2: 1

1: 1

None of these
diffcult
Solution
1: 1
A_{i} = A wins in i^{th} try
B_{i} = B wins in i^{th} try
⇒ P(A wins) = P(A wins in 1^{st} attempt) + P(A wins in 2^{nd}attempt)+…..∞
The above series is a G.P. with infinite terms, where common ratio
⇒ P(B wins) = 1 – P(A wins) (âˆµ There is no possible of draw)
It is given that P(A) = 2P(B)
SIMILAR QUESTIONS
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