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(#M40018135) ELITMUS Numerical Ability question quant Keep an EYE

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

Asked In Elitmus mahesh guntumadugu (11 years ago)

Unsolved Read Solution (7)

Is this Puzzle helpful?   (35)   (11) Submit Your Solution Permutation and Combination

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ASHISH KUMAR MISHRA  (10 years ago)

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

Is this solution Helpfull? Yes (20) | No (7)  

sarab  (11 years ago)

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

Is this solution Helpfull? Yes (10) | No (7)  

Debanu Das  (11 years ago)

d) 3:2 Win(Red) M/(M+N)=3/5 or Lose(Yellow) N/(M+N)=2/5

Is this solution Helpfull? Yes (5) | No (11)  

Siddartha Mulumudi  (10 years ago)

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

Is this solution Helpfull? Yes | No (5)  

Ayush Barnawal  (7 years ago)

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..

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  (7 years ago)

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)

Is this solution Helpfull? Yes | No (1)  

akshay kharade  (6 years ago)

P(WIN)=3/5
NOW SOLVE THE GP AND CALCULATE M:N.

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