Question

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 the ratio a : b is -

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. None of these

Answer 1

Answer: (C)

2 : 1

Answer 2

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

P (W) = , P(2) =

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

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

$\frac { ( a + b ) } { a + 2 b }$

Also P (B wins the game)= 1 – $\frac { b } { a + 2 b }$

According to the given condition,

$\frac { a + b } { a + 2 b }$ = 3. $\frac { b } { a + 2 b }$Ž a = 2b Ž a : b = 2 : 1