Abhishek and Aishwarya pick up a ball at random from a bag containing M red and N yellow coloured balls.one after the other,replacing the ball every time tillone of them gets a red ball.The first one to get a red ball is declared the winner.If Abhishek begins the game and the odds in favour of his winning the game are 3 to 2, then find the ratio M:N?
a)1:1 b)1:2 c)2:3 d)3:2

• Let Abhisek be winner Ok Now for Win he Must get red Ball for this :-
  P(Win)=M/(M+N)+N/(M+N)*N/(M+N)*M/(M+N)+.........=M/(M+N)/1/(N/(M+N)-1)
  For Abhishek to loose ......
  P(Loose)=MN/(M+N)*(M+N){1+N/((M+N)*(M+N))+...............
  Odd in Favour = P(Win)/P(Loose)=(M+N)/MN=3/2=> 1:2
• 10 years agoHelpfull: Yes(20) No(7)
• odds in favour of an event = (prob. that an event will occur)/(prob. that an event will not occur)
  
  here probability that an event will occur= m
  probability that an event will not occur= n
  odds in favour of his winning the game = m/n
  therefore ratio m:n =3/2
• 11 years agoHelpfull: Yes(10) No(7)
• d) 3:2 Win(Red) M/(M+N)=3/5 or Lose(Yellow) N/(M+N)=2/5
• 11 years agoHelpfull: Yes(5) No(11)
• I go with Abhishek Kumar Mishra. Who considered all the cases. Rest all took only 1st case.... The probality of Abhishek picking the red ball varies from Chance 1 to chance infinite. He may win in any of the chances
• 10 years agoHelpfull: Yes(0) No(5)
• https://www.quora.com/A-and-B-pick-up-a-ball-at-random-from-a-bag-containing-M-red-and-N-yellow-balls-one-after-the-other-replacing-the-ball-till-one-of-them-gets-a-red-ball-The-first-one-to-get-a-red-ball-is-the-winner-A-begins-the-game-and-the-odds-in-favor-of-his-winning-the-game-are-3-and-2-What-is-the-M-N-ratio
  
  Refer to this detailed Solution..
• 7 years agoHelpfull: Yes(0) No(0)
• let Abhishek wins the game,then let this event be E,
  p(E)=M/(M+N)+ N^2M/(M+N)^2 +N^4M/(M+N)4+.....
  solving this infinite G.p we get,
  p(E)=(M+N)/(M+2N)
  so, p(E(not))=1-p(E)=>N/(M+2N)
  a/q
  p(E)/p(E(not))=3/2
  (M+N)/N=3/2
  M:N=1:2(ans)
• 7 years agoHelpfull: Yes(0) No(1)
• P(WIN)=3/5
  NOW SOLVE THE GP AND CALCULATE M:N.
• 6 years agoHelpfull: Yes(0) No(0)