Question

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

Answer 1

I think the answer is 3:2

Hope it helps

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Answer 2

M:N = 1:2

GIVEN: Abhishek and Aishwarya pick up a ball at random from a bag containing M red and N yellow colored balls. one after the other, replacing the ball every time until one 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 favor of his winning the game are 3 to 2.
TO FIND: Ratio of M: N
SOLUTION: As we are given,
P(Abhishek winning the game) = 3/5.

Now it has been said that the game is played in turns and in each turn A will surely get a chance to pick a ball if that turn occurs.

Therefore,

The probability of Abhishek winning in each turn would be,

Turn 1: M/(M+N)

Turn 2: N/(M+N) * N/(M+N) * M/(M+N)

Turn 3: N/(M+N) * N/(M+N) *N/(M+N) * N/(M+N) * M/(M+N)

.

.

.

and this pattern keeps on.

Therefore,

P(Abhishek winning the game) =

P(Abhishek winning in turn 1) or P(Abhishek winning in turn 2) or P(Abhishek winning in turn 3)

Also,

P(A winning the game)= (M+N)/(M+2N)=3/5

Therefore,

M/N=1/2

M: N = 1: 2

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