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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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Solution answers | Comment 1 of 5

Answers : formula for N tokens: 1/N,  1/5 for 5 tokens .

Common sense justifies those results, and math supports them:

p= .2+.2*.8*2 +.2*(.8^2)*3+(.2*.8^3)*4+... 2*.8^(n-1)*n

LIM(P,n==> infinity) =5   

The result for N TOKENS  is  1/N.

btw- I have published a similar problem on this site regarding one true key among n keys - what is the probability that the right key will be the last one, if we try one by one...

  Posted by Ady TZIDON on 2016-07-18 15:03:26
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