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You have n items, with probability of .05, .1, .3 ..p(n).. = 1 = 100%

How can you calculate the expected amount of tries to get all items since they have unequal probability?

Then how can you calculate the expected amount of tries once you take out an item after it's been received x times?

In other words, once you get an item x times, it's probability changes to 0 causing all other items to shift accordingly.

If you have three items, .25 .25 .50. Then take out the .50 item, your chances of getting one of the last two items becomes .50 and .50.

Keanu Concepcion
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  • Can you specify the probabilities more precisely? There is not a clear pattern from $\frac1{20}, \frac1{10}, \frac3{10},\ldots, p_n$. – Math1000 Jan 10 '20 at 22:42
  • @Math1000 I just mean that you have a probability of anything you want. Just meant to illustrate that each of the n items have different probability – Keanu Concepcion Jan 10 '20 at 22:48
  • See relevant question for part (1): https://math.stackexchange.com/questions/3474643/coupon-collectors-variation-with-unequal-probabilities-and-uneven-number-of-ite https://math.stackexchange.com/questions/600012/coupon-collectors-problem-with-unequal-probabilities?rq=1

    TL;DR: Non-uniform coupon collector is hard to solve exactly, but can be estimated by focusing on the rarest events.

    After a cursory search, I haven't found a question that addresses the draw-dependence yet.

     – dusky Jan 10 '20 at 22:49
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    This question, asked yesterday, is pretty much the same. I think these are best answered by simulation, since they seem very arduous to do exactly. – saulspatz Jan 10 '20 at 22:59

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