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The First Repeat (Posted on 2016-07-18) Difficulty: 3 of 5
A bag has 5 tokens numbered 1 to 5. Tokens are drawn with replacement until a token is repeated. What is the probability that the repeated token is the first token drawn?

What is the formula for N tokens?

No Solution Yet Submitted by Brian Smith    
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re: answers | Comment 3 of 5 |
(In reply to answers by Ady TZIDON)

The difference between this problem and yours is that in this case, internal matches can halt the game prematurely.

Take for example n=2. The probability of matching the first draw is already 50% at the second draw. There's a 50% chance it did not match the first, and then the third draw terminates the game: either it matches the first or the second draw.  So there's 50% probability of a 2-draw game, with a successful match of draw 1; a 25% probability of a successful match of draw 1 on draw 3; and a 25% probability of a non-match of draw 1, as the third draw matches draw 2. The probability is 3/4, not 1/2.

  Posted by Charlie on 2016-07-18 15:13:55
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