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I have a pool of 36 samples (each is a pool itself). If I take a subset of eight samples at random from this pool, how do I calculate the probability of obtaining two of the same type of sample from the eight?

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Welcome to Math.SE. Thank you for your question. To help us to better answer it, please share the context (i.e. where it comes from). Also, please share what your thoughts are, and any progress you've made. If this is homework please [tag] it as such. – vadim123 May 29 '13 at 1:07
You have a population of 36 entities. You take two samples (with replacement) of size 8. You want to know the probability there is at least 1 entity both your samples have in common? – oldrinb May 29 '13 at 1:09
@oldrinb: I have a population of 36 entities (each of which is found many times in the pool). I take one sample of size 8. I want to know the likelihood of getting two of the same entity from the eight. – Kamza May 29 '13 at 1:49
Is the probability of picking any given entity uniformly distributed? – Zen May 29 '13 at 1:54
The probability of picking all different entities in the eight is $(\frac{1}{36})^8$ so the probability of obtaining at least one pair is $1-(\frac{1}{36})^8$. – Zen May 29 '13 at 2:01

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