probability win and loss

Question

There are 2 players , say A and B . There are m+n+1 cards and A gets m cards and B gets n cards. 1 card is left behind. A personality is linked with each card. The game begins as A begins to guess the left out card . If B has the card, he has to show the card. Else the judge checks the result if A is sure of his guess. Next turn goes to B . The game proceeds in this way. Now , what is the probability that A will win ? The probability must be accurate to 9 decimal places.

ans:0.500000000

Comments

1/n+1    +    n/n+1  *  m/m+1 *  1/n+1     +      n/n+1* m/m+1 * n/n+1 * m/m+1 * 1/n+1        + ......... So on

i'm not sure if this is correct or not, but it can be like this right?

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@Utkarsh After every try, effective number of cards reduce rt?

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oh yes!

1/n+1    +    n/n+1  *  m/m+1 *  1/n    +      n/n+1* m/m+1 * n-1/n* m-1/m * 1/n-1      + ......... So on

i guess this is correct!