I have a problem dealing with expected values. I'll jump right into the problem:(adsbygoogle = window.adsbygoogle || []).push({});

There are 3 red and 1 black balls in an urn. What is the expected number of times a ball must be removed before a black ball is removed.

I originally thought of this using

E[X]=1*P(X=1) + 2*P(X=2) + ...

I filled in P's using hyper geometric distribution. But didn't get the correct result.

Trying a uniform for each trial I did this

1*1/4 + 2*1/3 + 3*1/2 + 4*1/1

I found the following as a solution from a LONG derivation of formulas:

k(r+b+1)/(b+1) where k=1 in this case.

From a problem setup the same but using negative hyper geometric.

This makes no sense to me. Is there some more simple way of thinking of this?

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# Expected tries to to remove ball from urn

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