Q).A Bag contains P white and Q black balls. Two players A and B alternately draw a ball from the bag, replacing the balls each time after the draw till one of them draws a white and wins the games. If A begins the game and the probability of A winning the game is 3 times that of B, than of the ratio P : Q is

a)3:4
b)4:3
c)2:1
d)1:2

• the probability that A wins is:
  (p/p+q)+(q/p+q)*(q/p+q)*(p/p+q)+..........till infinity
  taking out p/p+q common and then applying the formula of infinite gp series we have
  
  P(A)=(p+q)/(p+2q).
  
  
  Now, finding the probability of B
  
  (q/p+q)*(p/p+q)+(q/p+q)*(q/p+q)*(p/p+q)+...........till infinity
  
  Taking out (q/p+q)*(p/p+q) common and applying the formula of infinite gp we have
  
  P(B)=q/p+2q
  
  NOW in the question it has been clearly mentioned that P(A)=3P(B)
  ...therefore by solving it we are getting the ratio to be 2:1(ANS)
• 10 years agoHelpfull: Yes(28) No(4)
• Sunny kumar genius
• 10 years agoHelpfull: Yes(6) No(3)
• 3:4
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• 9 years agoHelpfull: Yes(1) No(1)