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2 Answers

3 votes
3 votes
Since the balls are put back with replacement, the probability will not change.

P(G) - probability for green ball | P(B) - probability for blue ball

P(G) = x/(x + y) | P(B) = y/(x + y)

M wins the game if either he draws in the first turn, or he draws a blue and N also draws a blue and then he draws a green in his turn. Thus, we will get a series like this :

P(M) = P(G) + {1 - P(G)} * {1 - P(G)} * P(G) + ...

Also given, P(M) : {1 - P(M)} = 2 : 1

which gives P(M) = 2/3

Using the above values, we put in the series and we get the relation.
2 votes
2 votes

P(M winning)=P(G)+(1-P(G)(1-P(G)P(G)+........                      (infinite gp)

                   =x/(x+y)+y/(x+y) y/(x+y)  x/(x+y).....

                   =x  (1/1-r)                     where r=( y/(x+y))2

                         =x (x+y)/x2+2xy+y2-y2

                         =x+y/x+2y

it  is given that  is equal to 2/3

x+y/x+2y=2/3

x=y

so ans is b

                         

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