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Let's assume that I have 7 different elements (A,B,C,D,E,F,G) and I have a bag with an infinite number of those elements.

Each time I pull from the bag I have an equal probability of getting one of the elements.

If I pull X times, what's the expected number of distinct letters I will have?

Kahel
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  • Supposing, that the description by OP matches the scenario where we roll a die with a certain number of faces (seven) a certain number of times (X), we find that the problem appeared at the following MSE link to 2140363. – Marko Riedel May 17 '18 at 22:48

1 Answers1

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Is the "number of non-duplicates" the number of distinct letters you pull out of the bag (so an integer $\le7$)?

If so, the probability you pick a given letter, say $E$, at least once is $1-(6/7)^X$. By linearity of expectation, the expected number of distinct letters you pick is $7(1-(6/7)^X)$.

Angina Seng
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  • Hi thanks for the answer. What I would like to know is if I pull 12 times for example how many distinct letters will I have? if I pull 120 times, how many duplicates will I have? I will edit the question to make it more clear – Kahel May 17 '18 at 19:28