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A bag contains a white and b black balls...

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`

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To solve the problem, we need to find the ratio of white balls (a) to black balls (b) in a bag, given that player A has three times the probability of winning compared to player B. ### Step-by-Step Solution: 1. **Define the Probabilities**: - Let \( P(A) \) be the probability that player A wins the game. - Let \( P(B) \) be the probability that player B wins the game. ...
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