Say we have NA blue balls and NB red balls mixed together in an urn. When we pick a ball it leaves the urn. I want to find the probability of picking n red balls in a row.(adsbygoogle = window.adsbygoogle || []).push({});

The probability of picking a red ball is:

NA/(NA+NB)

But each time a red ball leaves the urn the probability of picking the next will be:

(NA-1)/(NA+NB-1)

So in general for n successive red ball picks the probability must be:

p(n) = ∏_{i=0}^{n}(NA-1)/(NA+NB-i)

First of all I want to ask if this is correctly deduced. Secondly, I want to know if you can evaluate a product like the above in a closed form.

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# Homework Help: Closed form expression for this?

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