Question

A bag contains a white and b black balls. Two players, A and B alternate ydraw 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, the ratio ab is

Solution

Correct option is

2:1

Let W denote the event of drawing a white ball at any draw and B that for a black ball. Then

                     

P (A wins the game) = (W or AAW or BBBBW or ……)

                                = (W) + (BBBBW) + …….

                                = P(W) + P(BP(BP(W) + P(BP(BP(BP(B)P(W) + ……

                                = (W) + P(W). (B) 2 + P(W). (B)4 + …..

                                

Also    P (B wins the game) 

According to the given condition,

                 

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