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?
(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